There are 4 questions here that need to be solved.
a. The velocity of the astronaut & book system after the collision (using conservation of momentum) is 0.19 m/s
b. The initial kinetic energy of the system is 24J
c. The final kinetic energy of the system is 1.14J
d. The impulse exerted by the book on the astronaut is 11.43 kg.m/s
What is kinetic energy?In physics, the kinetic energy of an object is the energy that it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during acceleration, the body maintains this kinetic energy unless its speed changes.
Now, let's answer the question.
a.
m1 book = 3kg
m2 astronaut = 60kg
vi1 = 4m/s
vi2 = 0m/s
Vf = final speed after collision
Now, let calculate using conservation of momentum formula
ρi = ρf
m1 * vi1 + m2 * v2 = (m1 + m2) * vf
3 * 4 + 60 * 0 = (3 + 60) * vf
12 = 63vf
vf = 0.19 m/s (rounded)
So, the velocity of the astronaut-book system after the collision is 0.19 m/s.
b. Initial kinetic energy will be calculated using kinetic energy formula
KEi = 1/2 * m1 * Vi1^2
= 1/2 * 3 * 4^2
= 24J
So, the initial kinetic energy of the system is 24J
c. Final kinetic energy will be calculated as follows
KEf = 1/2 * (m1 + m2) * vf^2
= 1/2 * (3 + 60) * 0.19^2
= 1.137J
So, the final kinetic energy of the system is 1.137J
d. To calculate the impulse, it is basically the change in momentum of the book, calculated as follows
I (impulse) = m1 * (Vi1 - Vf)
= 3 * (4-0.19)
= 11.43 Kg.m/s
Therefore, the impulse exerted by the book on the astronaut is 11.43 Kg.m/s
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What is the average velocity between 12. 00 and 15. 00 seconds? 81. 0 m/s, east 27. 00 m/s, east 9. 00 m/s, east 0. 0123 m/s, east.
The average velocity between the time interval is 27 m/s east that is option B is correct.
Velocity is a vector quantity that is it has both magnitude as well as direction and it can be represented as
Velocity = Displacement/Time
The unit of velocity is m/s. Average velocity is the ratio of the change in displacement to the change in time. Now, If we look at the graph
The Displacement of the object in the graph after 12.00 seconds = 144 m
The Displacement of the object in the graph after 15.00 seconds = 225 m
Average velocity = Change in displacement/Change in time
Average velocity = (225 - 144)/(14 - 12)
Average velocity = 81/3
Average velocity = 27m/s
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a simple pendulum consisting of a bob of mass m attached to a string of length l swings with a period t.
Due to their mutual free fall, the pendulum as well as the position to which it is linked will no longer oscillate.
What are the uses of a pendulum?Pendulum a body that is hanged from a fixed location and moves back and forth as a result of gravity. Pendulums are employed to control clock movement because the period the amount of time between each full oscillation is constant.
Briefing:We will utilize the concept of the duration in a basic pendulum to tackle this issue, which cautions that it depends on the length and gravity of the pendulum:
T = 2π√(L/g)
Here,
L = Length
g = Acceleration due to gravity
T = √(L/g)
Since 2π is a constant, we can deduce that its proportionality towards the square root of the its lengths over its gravity is 2.
g→ 0 ⇒ T→∞
The object is in continuous free fall, or in a situation where gravity is typically zero.
The period's value will eventually approach infinity. As a result of the pendulum's attachment point also being in free fall, it means that the pendulum would no longer oscillate.
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Which of these substances contains a compound made up of exactly 2 different types of atom?.
The substance which contains a compound made up of exactly 2 different types of atom is A)water.So,correct option is A.
In the least difficult of terms, a chemical compound is a kind of substance, and molecules make up synthetic mixtures. At the point when particles of more than one kind bond together in a proper proportion, they structure compounds. Synthetic responses can break compounds into the components that form them. Mixtures may likewise separate into less complex mixtures.
Compounds are Unique in relation to Components and Combinations. Atoms are the least difficult particles of issue that have particular synthetic properties. Researchers at present perceive 118 individual kinds of molecules or components.
Water is made up of 2 hydrogen atoms and oxygen atoms. Its chemical formula is H₂O.
Hence, correct option is A.
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primary producers are present in every biome, including the deep sea. how can primary producers exist in the deep sea when sunlight does not penetrate to these depths?
Primary producers can exist in the deep sea when sunlight does not penetrate to these depths because primary producers in the deep sea use energy from chemical reactions to drive the reduction of carbon dioxide to organic compounds.
In the field of biology, primary producers can be described as organisms that can make their own food by reducing carbon dioxide in the presence of sunlight.
However, there are primary producers present in the deep sea that do not require sunlight for the production of food or organic compounds. This is because the primary producers that are present in the deep sea have the ability to derive energy from chemical reactions that will reduce carbon dioxide to produce organic compounds from it. These organic compounds can be used as a source of energy.
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A 3. 00-kg rifle fires a 0. 00500-kg bullet at a speed of 300 m/s. Which force is greater in magnitude: the force that the rifle exerts on the bullet or the force that the bullet exerts on the rifle?.
Answer:
Forces are equal
Explanation:
The forces are equal in magnitude and opposite in direction. This is Newton's 3rd Law of Motion.
unlike signal transduction in many other sensory receptors, signal transduction in rods
Photoreceptors, in contrast to most sensory receptor cells, have a hyperpolarization response to stimulation and a depolarization response to inhibition. This indicates that when the cell is not activated, glutamate is constantly released; but, when the cell is triggered, release ceases.
What occurs when light impinges on a rod?As I previously stated, if a light ray strikes rhodopsin as it enters the eye and strikes a rod, it will really start a phototransduction cascade that causes the rod to fire an action potential. In a cone, the identical procedure takes place.
Cones and rods provide visual signals to bipolar cells, which send them on to ganglion cells. The retina itself is where a significant portion of visual information processing takes place.
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When the spring is stretched and the distanced from point A to point B is 5.2 feet, what is the valuue of 0 to the nearest tenth of a degree?
(A) The distance from point A to point B to the nearest tenth of a foot will be 3.4 ft.
(B) The value of 0 to the nearest tenth of a degree will be 54.8°
SOH, CAH, and TOA are the trigonometry ratios that need to be solved in order to find necessary measures or angles in a right triangle.
A) Reference angle = 28 degrees
Distance A-B = ?
Adjacent = 3 ft
We will calculate the distance between A-B by using the trigonometry function, CAH, that is:
Cos ∅ = adj ÷ hyp
Cos 28° = 3 ÷ A-B
A-B = 3 ÷ Cos 28°
A-B = 3.4 ft
B) Reference angle = ?
Distance A-B = 5.2 ft
Adjacent = 3 ft
We will calculate the distance between A-B by using the trigonometry function, CAH, that is:
Cos ∅ = adj ÷ hyp
Put the values
Cos ∅ = 3 ÷ 5.2
∅ = Cos⁻¹ (3 ÷ 5.2)
∅ = 54.8°
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Which of the following is(are) true of globular clusters?
A. They are smaller groups of stars orbiting larger galaxies.
B. The stars in them are all of roughly the same age.
C. Both a and b are correct.
Answer:
B
Explanation:
the others don’t seem right
What is the frequency of wavelength 500 m?
The frequency of wave is 0.6×10⁶Hz if 500m is the wavelength of the light wave.
Frequency is defined as the rate at which current takes an alternate route each second. It is estimated in hertz (Hz), a global unit of measure where 1 hertz is equivalent to 1 cycle each second. The inverse of frequency is known as spatial frequency.
For electromagnetic wave ,we have an expression
c=ν × λ
where c is the defined as the speed of wave in any medium,
ν is defined as the frequency of the wave and
λ is defined as the wavelength of the wave.
Since wave is light wave so speed(c) of light =3×10⁸m/sec,
frequency=? and wavelength=500m
Therefore,3×10⁸m/sec=v×500
=>v=(3×10⁸)/500
=>v=0.6×10⁶/sec
or=>v=0.6×10⁶Hz.
Hence, frequency of light wave is 0.6×10⁶m.
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(Complete question) is:
What is the frequency of wave having wavelength 500m.Assume wave is a light wave?
"A sound of frequency 15Hz and an amplitude of 70dB is inaudible." Explain with reasons if this statement is true or false.
A sound of frequency 15Hz and an amplitude of 70dB is inaudible. This is true statement.
What is audible sound?The human ear can easily hear frequencies between 20 Hz and 20 kHz. Therefore, sound waves with a frequency between 20 Hz and 20 kHz are regarded as audible sound. The human ear may be able to pick up on even the smallest changes in air pressure if they are in the audible frequency range. The difference in air pressure is less than one billionth of a percent.
As we age and are exposed to sound for extended periods of time, the upper limit of our hearing frequencies decreases. A typical middle-aged adult can hear well up to 12 to 14 kilohertz, which is the highest frequency.
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which electromagnetic radiation wavelength is efficiently observed using ground based telescopes?
Radio is the electromagnetic radiation wavelength that is efficiently observed using ground-based telescopes.
Most telescopes under $150 have poor optical quality and aren't worth much. Instead, I recommend getting good binoculars. Stay away from telescopes advertised as having high magnification. The most important feature of a telescope is its size and the diameter of the primary mirror or lens. With a diameter of 4 or 5 inches.
The telescope is ideal for viewing solar system objects such as planets, moons, and moons of Jupiter. There are three main types of astronomical telescopes. Refractor telescope, Newton telescope, and Schmidt-Cassegrain telescope. It can damage not only your eyes but also your telescope lens.
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What is potential energy of a spring if the spring is constant?
It is the potential energy stored in spring when it is stretched or deformed. It is equal to force multiplied by displacement. This energy is stored in the spring by virtue of its position. It is the work done to stretch the spring.
When spring is stretched, it undergoes displacement. It comes to its equilibrium position when force is removed. So, it exerts an equal and opposite force When it is stretched. Work is done by this force that is stored in the form of potential energy.
Since potential energy = force × displacement
and, force = spring constant × displacement
So, potential energy = spring constant × [tex](displacement)^{2}[/tex]
P.E. = k ×[tex]x^{2}[/tex]
Where,
k = spring constant
x = displacement caused due to stretching
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Questions
Q1.
A teacher takes a group of students on to a sports field to measure the speed of sound in air.
The teacher fires a starting pistol.
It produces a loud bang and a flash of light at the same time.
The students take measurements.
Describe how the measurements are made and used to determine the speed of sound in air.
Answer:
Below
Explanation:
Measure distance to pistol .....
speed of light is nearly instantaneous in this situation (short distance)
measure time from flash to hearing the sound
speed of sound = distance to pistol / time to hear
an intergalactic spaceship arrives at a distant planet that rotates on its axis with a period of t. the spaceship enters a geosynchronous orbit at a distance of r.
The spaceship enters a geosynchronous orbit is M = 4π 2 R 3 /GT 2 M = 1.35 × 10²⁸ kg.
A geostationary orbit is a low-inclination prograde orbit around the Earth lasting 23 hours 56 minutes and 4 seconds. A spacecraft in a geostationary orbit appears to move north and south but appears to stay at a fixed longitude on Earth. A geostationary orbit is a geostationary orbit.
A geostationary satellite orbit is an orbit around the Earth that intentionally has an orbital period of one sidereal day equal to the Earth's sidereal rotation period, with the satellite returning to the same position in the sky after each sidereal day. Geostationary means that the satellite orbits with the same angular velocity as the earth.
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if the magnitude of the magnetic field is now decreased at a rate of -0.16 t/s , what force (magnitude and direction) will act on q ?
The magnitude of the force acting on q will be 0.16 t/s times the magnitude of the charge q, and it will be in the opposite direction of the magnetic field.
The force on a charged particle in a magnetic field is given by the equation:
F = qv × B
where q is the charge of the particle, v is the velocity of the particle and B is the magnitude of the magnetic field.
When the magnitude of the magnetic field is decreased at a rate of -0.16 t/s, the force on the particle will be in the opposite direction of the decreasing magnetic field. This is because the magnitude of the magnetic field will be decreasing over time, so the force on the particle will be in the opposite direction of the decreasing magnetic field.
The magnitude of the force acting on the particle will be equal to the product of the charge of the particle and the velocity of the particle multiplied by the rate of change of the magnetic field. That is, the magnitude of the force will be:
F = qv × (-0.16 t/s)
The direction of the force will be in the opposite direction of the decreasing magnetic field.
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communications satellites would fly off in a straight line never to be see again if it were not for a force from the earth compelling them to constantly change their direction. this tendency to fly off in a straight line is a statement of the
Communications satellites would fly off in a straight line never to be see again if it were not for a force from the earth, The moon "falls" from a straight line because there IS some attraction toward the Earth.
What would happen if forces were suddenly removed from the satellite?The satellite will tend to move tangential to the initial orbit without the assistance of centripetal force at the same speed as it did just before the gravitational field vanishes. As a result, the spacecraft will veer off course and leave its orbit.
Do people gravitate toward one another?The combined gravitational force of acts on the mass in your body. What gives you weight is that. Additionally, you would weigh less than you do now if you were on a planet with a lower mass than Earth. You make the same gravitational force on Earth that it does on you.
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The chemical formula for carbonic acid, a compound used in carbonated drinks, is H2CO3. Assume that these symbols represent the three elements of this compound:
Three atoms, grey represents carbon, red represents oxygen and white represents hydrogen
Which picture correctly represents carbonic acid?
A.
Molecule structure has five atoms connected in a straight line using single bond in order of white atom, red atom, grey atom, red atom and white atom. The grey atom in center is connected to a red atom in double bond
B.
Molecule structure has five atoms connected in a straight line using single bond in order of Red atom, white atom, grey atom, white atom and red atom. The grey atom is connected to a white atom in double bond
C.
Molecule structure has five atoms connected in a straight line using single bond in order of Red atom, white atom, grey atom, white atom and red atom. The grey atom is connected to a white atom in double bond
D.
Molecule structure has five atoms connected in a straight line using single bond in order of Red atom, grey atom, white atom, grey atom and red atom. The white atom in center is connected to grey atom in double bond
The picture that correctly represents carbonic acid is:
A molecule structure has five atoms connected in a straight line using a single bond in order of white atom, red atom, grey atom, red atom, and white atom. The grey atom in the center is connected to a red atom in a double bond.
The correct option is A.
What is the structure of carbonic acid?Carbonic acid is a weak acid that is used in carbonated drinks.
The molecular formula for carbonic acid is H₂CO₃.
The formula shows that a molecule of carbonic acid is composed of two atoms of hydrogen, one atom of carbon, and three atoms of oxygen.
Like other acids, it reacts with bases to form salt and water. In addition, carbon dioxide is produced when carbonic acid reacts with bases.
The structure of carbonic acid shows that a single atom of carbon is linked to three atoms of oxygen. One of the bonds of carbon with an oxygen atom is a double bond while the other two are single bonds. The oxygen atoms that are bonded to carbon by means of single bonds are then bonded to one hydrogen atom each.
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what is the magnetic field amplitude b0 of an electromagnetic wave that has an electric field amplitude e0 of 0.365 v/m ?
The amplitude of the magnetic field for the given electromagnetic waves is [tex]1.21 * 10^{-9}[/tex] T.
For electromagnetic waves the relation between electric field amplitude and magnetic field amplitude is given as
[tex]\frac{e_{0} }{b_{0} } = c[/tex]
where c is the speed of light in free space i.e. [tex]3 * 10 ^{8}[/tex] m/s.
Finding the amplitude of the magnetic field for the given question by substituting the values in the given relation :
[tex]b_{0} = \frac{e_{0} }{c}[/tex]
[tex]b_{0} = \frac{0.365}{c} = 1.21 * 10^{-9}[/tex] T
Electromagnetic waves are produced when an electric field interacts with a magnetic field. The term "electromagnetic" is used to describe them. The magnetic and electric fields of an electromagnetic wave are parallel (at right angles). They also follow the direction of the EM wave, but perpendicularly.
There is no redirection of them by electric or magnetic fields. Diffraction and interference are possible with EM waves.
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a crate is supported by two ropes. one rope makes an angle of with the horizontal and has a tension of lb on it. the other rope is horizontal. find the weight of the crate and the tension in the horizontal rope.
A crate is supported by two ropes. one rope makes an angle of with the horizontal and has a tension of lb on it. the other rope is horizontal. Weight of the crate m kg and the tension is T in the horizontal rope.
The pulling force conveyed axially by a string, rope, chain, or other similar object, or by each end of a rod, truss member, or other related three-dimensional object is known as tension in physics. The action-reaction pair of forces acting at the ends of the aforementioned elements is another way to define tension. Perhaps tension is the polar opposite of compression. A restoring force may cause what is also referred to as tension when atoms or molecules are torn apart from one another at the atomic level and build up potential energy. Each end of a string or rod may pull on the object it is attached to in an effort to alleviate the tension while it is under such pressure. To measure tension as a transmitted force, an action-reaction pair of forces, or a restoring force, the International System of Units (SI) utilizes newtons (or pounds-force in Imperial units).
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Displacement vectors of 4 km south, 2 km north, 5 km south, and 5 km north combine to a total displacement of: ________
The total displacement of the vectors is 2 km south.
Distance is the total path that an object in motion has traveled. Displacement is a verb that denotes the movement or displacement of an object.
Here, the vector moves 4 km towards the south, then moves 2 km north. The vector again moves 5 km south and moves 5 km north. Draw the diagram, mentioning the 4 km south movement by the black arrow, the 2 km north movement by the blue arrow, the 5 km south movement by the orange arrow, and the 5km north movement by the green arrow.
Also, mark the starting and ending points. These points give the displacement of the diagram. From the diagram, we can tell, the displacement is 2 km south of the starting point.
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since the observer does not interact with the subject in observation studies, observation is an error-free method of data collection question 2 options:
Ans is false. There are several errors associated with observation: subjectivity, observer bias, accuracy, and interpretation.
How to find error free method of data collection?Observational error (or measurement error) is the difference between a measured value of and its true value.
The errors associated with data collection, mentioned above can be defined as follows:
1. Subjectivity bias : the tendency of participant in a study to react, either consciously or unconsciously. Here they act experimentally and not naturally.
2. Observation bias : the tendency of observers to not see what is there, but instead to see what they expect or want to see.
3) Accuracy : the condition or quality of being true, correct, or exact; freedom from error or defect; precision or exactness; correctness.
4) interpretation: can be defined as understanding of something. One can avoid it by using multiple sources of information, such as references and personal interviews,
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what happens when two oceanic plates diverge?
Divergent plate boundaries are where two plates are shifting apart from one another. Rising magma from the core of the Earth at these boundaries erupts, forming a new layer on the lithosphere. Ocean-spreading ridges are submerged mountain ranges that are formed by the majority of divergent plate borders.
What is a Divergent Plate Boundary?A diverging boundary, also referred to as a divergent boundary, is a linear structure that occurs between two tectonic that are moving apart in the field of plate tectonics. It is sometimes referred to as a constructive barrier or an extensional border.
Rifts are initially created by divergent plate boundaries within continents; they later develop into rift valleys. Oceanic plates' mid-oceanic ridges are where the majority of active plate boundary borders are found.
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an anchor rope to anchor a ship to the pier is wrapped 2 full times around a support on the ship. a deck hand can keep the rope from slipping by applying a force of 100 n to the free end. what is the coefficient of friction between the rope and the support?
The coefficient of friction = 0.34 between the rope and the support.
This type of question can be solved using Capstan's equation,
Capstan's equation is generally used to calculate the friction of the coefficients or the yarns. Represented as-
[tex]T_{1} = T_{0}e^{u}[/tex].
Now according to the term coefficient of friction, we calculate the friction between any two surfaces. It is also referred to as the ratio of the resistive force to the normal force.
The Capstain's equation is given by-
[tex]T_{load} = T_{hold} e^{uo}[/tex]
u is given as μ and o denotes Φ
the load = 7000
hold support is 100N
Φ = 2[tex]\pi[/tex] for the whole rotation
Since the rope is wrapped 2 times = 4[tex]\pi[/tex]
7000 = 100[tex]e^{u4\pi }[/tex]
log on both sides
⇒ u = log 7000/ 100*4[tex]\pi[/tex]
⇒ u = 0.338
Therefore, the coefficient of friction between rope and support = 0.34
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an object is released from a stationary hot balloon at height h above the ground. an identical object is released at height h above the ground from another balloon that us rising at constant speed. air resistance is negligible. what does not increase for the object released from the rising balloon?
Whether the object is released from the stationary hot balloon or moving hot balloon, its acceleration is neither increased nor decreased because acceleration due to gravity "g" is constant or has a constant value.
When an object is released from the stationary hot balloon at a height h above the ground and an identical object is released at heigh h above the ground from another balloon that is rising at a constant speed, there is no difference in its acceleration compared to the previous one. This is because the acceleration due to gravity, denoted as 'g' is constant at the value of 9.8 m/s.
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the driver of a motorboat that can move at 10 m/s in still water wishes to travel directly across a narrow strait in which the current flows at 5.0 m/s. at what angle upstream should the driver head the boat?
The angle of the upstream of the driver of the boat is 30°
The velocity of the boat = Vb = 10m/s
The velocity of the water in the river = Vw = 5m/s
θ = [tex]sin^{-1}[/tex] (Vr/Vb)
θ = [tex]sin^{-1}[/tex] (5/10) = 30°
Upstream refers to a boat that is moving against the flow of the stream. The term " speed" in this context refers to the boat's net speed. Downstream. A boat is said. to be moving downstream if it is moving. in the same direction as the stream. A stream is the name for the flowing water. in a river. The difference when speaking about water in rivers and streams is that upstream, also known as upriver, is in opposition to the water flow and in the direction of the water's original source (where the river originates). For instance, a boat can navigate upstream against the river's downward flow.
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The planet Earth orbits around the Sun and also spins on its own axis.
a) Calculate the angular momentum, in kilogram meters squared per second, of the Earth in its orbit around the Sun.
b) Calculate the angular momentum, in kilogram meters squared per second, of the Earth spining on its axis.
c) How many times larger is the angular momentum of the Earth in its orbit than the angular momentum of the
Earth spinning on its axis?
In its orbit around the Sun, Earth has an angular momentum of 2.661 1040 kg/m2/s.
what is angular momentum?A rotating object's property that is determined by its moment of inertia multiplied by its angular velocity is known as angular momentum. It is a characteristic of rotating bodies determined by their combined moments of inertia and angular velocities.
What governs angular momentum?In the equation for angular momentum, L stands for angular momentum, I for rotational inertia, and (the Greek symbol omega) for angular velocity. This can be put more simply by saying how an entity's angular momentum is equal to the sum of its mass, speed, and separation from the point of rotation.
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9. The Matt Schaub drops back 10 yards to throw a pass. He throws the pass 10 yards
of the to Daniels who gets tackled right there. What is the total displacement of the football?
The total displacement of the football is 20 yards.
What is displacement?
Displacement is defined as the change in position of an object.
Displacement is a vector quantity and has a direction and magnitude.
The calculate the total displacement of the football, we will determine the change in the position of the ball as shown below.
Δx = xf - xi
where;
xf is the final position of the footballxi is the initial position of the footballΔx = ( 10 yards + 10 yards ) - ( 0 yards )
Δx = 20 yards
Thus, the total displacement of the ball is a function of initial and final position of the ball.
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Why is kinetic energy called the energy of motion?
Kinetic energy refers to a part of internal energy where immobility refers to potential and movement occurs with velocity as KE=mv²/2.
Kinetic energy depends on the velocity of an object and is the ability of a moving object to act on other objects when colliding with them. On the other hand, the kinetic energy of an object represents the amount of energy required to increase the velocity of the object from rest (v = 0) to its terminal velocity. Kinetic energy is a numerical measure of the inertia of an object and is also linearly related to mass, a measure of the object's resistance to acceleration when a force is applied.For a body of revolution, the moment of inertia I corresponds to mass and the angular velocity (ω) corresponds to linear or translational velocity. Therefore, the kinetic energy of rotation is equal to half the product of the moment of inertia and the square of the angular velocity.The total kinetic energy of an object or system equals the sum of the kinetic energies resulting from all kinds of motion.To understand more about Kinetic energy -
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an object is located midway between the focal point and the center of a concave spherical mirror. draw a ray diagram to locate its image. is the image real or virtual, erect or inverted, magnified or reduced in size?
At the concave mirror's center of curvature, something is situated. The picture is accurate and reversed.
For a concave mirror, the object-image connection is given by,
1 ÷ s + 1 ÷ s' = 2 ÷ R
the object distance, where s
The picture distance is s'.
The radius of curvature is R.
Now, the distance between an item and the point of curvature equals the radius of curvature.
s = R
Using s = R as a substitute and solving for s'
s' = [tex]((\frac{2}{R} ) - (\frac{1}{s} ))^{-1}[/tex]
s' = [tex]((\frac{2}{R} ) - (\frac{1}{R}))^{-1}[/tex]
s' = [tex]{(\frac{1}{R})}^{-1}[/tex]
s' = R
As a result, the photograph is real and can be found at R.
We discovered that the picture is genuine and is not at infinity.
Sideways magnification is
m = y' ÷ y = -s' ÷ s
where y is the height of the item.
The picture height is y'.
calculating the magnification
m = -s' ÷ s
= -R ÷ R
m = -1
As a result, the image size doesn't change.
We discover that neither the image's size nor its size has been changed.
calculating the picture height now
y' = my
y' = -y
Consequently, the picture is reversed.
The picture is not upright, as we discover.
The only accurate response to the query utilizing the outcomes is that the image is Real.
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an electron and a 0.0320-kg bullet each have a velocity of magnitude 510 m/s, accurate to within 0.0100%. within what lower limit could we determine the position of each object along the direction of the velocity?electron mmbullet m
for this we apply, Heisenberg's uncertainty principle.
it states that physical variables like position and momentum, can never simultaneously know both variables at the same moment.
the formula is,
Δp * Δx = h/4π
m(e).Δv * Δx = h/4π
by rearranging,
Δx = h / 4π * m(e).Δv
Δx = (6.63*10^-34) / 4 * 3.142 * 9.11*10^-31 * 5.10*10^-2
Δx = 6.63*10^-34 / 583.9 X 10 ⁻³¹
Δx = 0.011 X 10⁻³
for the bullet
Δx = (6.63*10^-34) / 4 * 3.142 * 0.032*10^-31 * 5.10*10^-2
Δx = 6.63*10^-34 /2.05
Δx =3.23 X 10⁻³² m
therefore, we can say that the lower limits are 0.011 X 10⁻³ m for the electron and 3.23 X 10⁻³² m for the bullet
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