Given data
*The given resistors are
[tex]R_1=R_{2_{}}_{}_{}=4\text{ ohm}[/tex]*The given battery voltage is V = 12 V
The equivalent resistance in parallel combination is calculated as
[tex]\begin{gathered} R_{eq}=\frac{R_1\times R_2}{R_1+R_2} \\ =\frac{4\times4}{4+4} \\ =\frac{16}{8} \\ =2\text{ ohm} \end{gathered}[/tex]The total current flows through the battery is calculated as
[tex]\begin{gathered} I=\frac{V}{R_{eq}} \\ =\frac{12}{2} \\ =6\text{ A} \end{gathered}[/tex]What is the area under the curve on the velocity time graph in physics represent
When given a graph of velocity vs time as the following:
The area under the curve represents the distance that the object has moved in the given time interval.
How much does James have to pay for a vaccum cleaner that he uses for 4 hours a week. In James's neighborhood, the cost of electricity is 27 cents per kwhr.The power is P = 800 W
Given:
The power of the vacuum cleaner is P = 800 W = 0.8 kW
The time consumption is t = 4 hours a week.
The cost of electricity is 27 cents per kWh
To find the cost of the electricity for using the vacuum cleaner for a week.
Explanation:
First, we need to find the energy.
The energy can be calculated as
[tex]\begin{gathered} E=P\times t \\ =0.8\times4 \\ =3.2\text{ kWh} \end{gathered}[/tex]The cost of electricity per week due to vacuum cleaner will be
[tex]27\times3.2=86.4\text{ cents}[/tex]Final Answer: The cost of electricity James has to pay for a vacuum cleaner for using it 4 hours a week is 86.4 cents.
How far will a bike travel if you pedal at 13 m/s for 7 seconds?
Given
[tex]\begin{gathered} v=13\text{ m/s} \\ t=7\text{ s} \end{gathered}[/tex]The distance covered is given as,
[tex]s=vt[/tex]Here, s is the distance travelled, v is the speed and t is the time .
Substituting all known values,
[tex]\begin{gathered} s=(13\text{ m/s)}\times(7\text{ s)} \\ =91\text{ m} \end{gathered}[/tex]Therefore, the bike will travel 91 m is 7 second.
A 0.24 kg blob of clay strikes a wall with an Initial velocity of 25 m/s the clay come to a stop against the wall in 91 ms what is the average impact force on the clay
ANSWER
65.9N
EXPLANATION
The impact force of an object is
[tex]F=\frac{\Delta p}{\Delta t}[/tex]And the change in momentum is
[tex]\Delta p=m(v_f-v_i)[/tex]We know that the mass of the blob of clay is 0.24kg, its initial velocity is 25m/s and its final velocity is 0m/s. Also, the time of the collision is 91 ms.
The force is:
[tex]F=\frac{m(v_f-v_i)}{\Delta t}[/tex]To be consistent with the units, we have to write the time in seconds, not milliseconds:
[tex]F=\frac{0.24\operatorname{kg}(0-25)m/s}{0.091s}[/tex][tex]F\approx-65.9N[/tex]This result is negative because this is the force the clay exerts on the wall. By Newton's third law, the impact force on the clay is the force with the same magnitude and opposite direction. Therefore, the average impact force on the clay is 65.9N
you have entered a 134-mile biathlon that consists of a run and a bicycle race. During your run, your average velocity is 6 miles per hour, and during your bicycle ace, your average velocity is 29 miles per hour. You finish the race in 7 hours. What is the distance of the run? What is the distance of the bicycle race?upposeWhat is the distance of the run?miles
ANSWER:
Distance of the run: 18 miles
Distance of the bicycle race: 116 miles
STEP-BY-STEP EXPLANATION:
Given:
Total distance = 134 miles
Total time = 7 hours
Average velocity during running = 6 mph
Average velocity during bicycle = 29 mph
Let x be the running distance and y be the bicycle distance.
We know that velocity equals distance in a given time, like this:
[tex]\begin{gathered} v=\frac{d}{t} \\ \\ \text{ Therefore:} \\ \\ t=\frac{d}{v} \end{gathered}[/tex]Knowing the above, we can establish the following system of equations:
[tex]\begin{gathered} t_1+t_2=7\rightarrow\frac{d_1}{v_1}+\frac{d_2}{v_2}=7\rightarrow\frac{x}{6}+\frac{y}{29}=7\text{ \lparen1\rparen} \\ \\ x+y=134\rightarrow x=134-y\text{ \lparen2\rparen} \end{gathered}[/tex]We substitute the second equation in the first and obtain the following:
[tex]\begin{gathered} \frac{134-y}{6}+\frac{y}{29}=7 \\ \\ \frac{(134-y)(29)+6y}{6\cdot29}=7 \\ \\ \frac{3886-29y+6y}{174}=7 \\ \\ 3886-23y=7\cdot174 \\ \\ y=\frac{1218-3886}{-23}=\frac{-2668}{-23} \\ \\ y=116\rightarrow\text{ bicycle distance} \\ \\ \text{ now, for x:} \\ \\ x=134-116 \\ \\ x=18\rightarrow\text{ running distance} \end{gathered}[/tex]Therefore:
The distance of running is 18 miles and the distance by bicycle is 116 miles.
The wire feed controls the amperage during the welding process. A control knob labeled in metric units shows a maximum wire-feed speed of 160 mm/sec. What is this maximum speed in inches per minute?The maximum speed is ___ inches per minute.
Answer: 378 inches per minute
Explanation:
We want to convert 160 mm/sec to inches per minute.
Recall,
1 mm = 0.03937 inches
1 second = 0.01667 minutes
Thus,
160 mm/sec = 160 x 0.03937 inches/0.01667 minutes
= 378 inches per minute
Could really some help answering this question I don’t really understand! :)
Given:
Object A is at a higher temperature than object B.
Here, there is a difference in temperature.
Temperature flow is similar to water flow.
The water stops flowing if the water level becomes the same in botht containers.
Similarly, thermal energy transfers between the objects until the objects have changed the temperature by the same amount.
Thus, option B is correct.
A proton is accelerated through a potential difference of 100 V and then enters a region where it is moving perpendicular to a magnetic field B = 0.20 T. Calculate the radius of the circular path in which it will travel.
The radius of the circular path in which it will travel inside the magnetic field will be 7mm.
Magnetic field is the area around a magnet or an electric charge in which the effect of magnetism is felt.
Magnetic field of the proton = B = 0.20 T
Electric potential difference of the proton = E = 100 V
Kinetic energy of proton = 100p = [tex]\frac{1}{2}m v^{2}[/tex]
[tex]v = \sqrt{\frac{2*100e}{m} }[/tex]
The centripetal acceleration is provided by the magnetic field.
therefore,
[tex]\frac{mv^{2} }{r} = evB[/tex]
mv = eBr
[tex]r = \frac{mv}{eB}[/tex]
m = 1.67 × [tex]10^{-27}[/tex] kg
e = 1.60 × [tex]10^{-19}[/tex] C
B = 0.20 T
v = [tex]\sqrt{\frac{2*100e}{m} }[/tex] = 13.8 × [tex]10^{4}[/tex] m/s
on putting the values of all the quantities in the equation of r, we get
r = 0.07 m
r = 7 mm
The radius of the circular path is 7 mm.
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Unbeknownst to most students, every time the school floors are waxed, the physics teachers get together to have a barrel of phun doing friction experiments in their socks (uhm - they do have clothes on; its just that they don't have any shoes on their feet). On one occasion, Mr. London applies a horizontal force to accelerate Mr. Schneider (mass of 84 kg) rightward at a rate of 1.2 m/s/s. If the coefficient of friction between Mr. Schneider 's socks and the freshly waxed floors is 0.35, then with what force (in Newtons) must Mr. London be pulling?
The frictional force is taken away from the net force. Mr. London will pull with a force of 388.9 N
What is Force ?Force can simply be defined as a pull or push. It is a product of mass and acceleration. It is a vector quantity.
Given that Mr. London applies a horizontal force to accelerate Mr. Schneider (mass of 84 kg) rightward at a rate of 1.2 m/s/s. If the coefficient of friction between Mr. Schneider 's socks and the freshly waxed floors is 0.35, then the force F in which Mr. London is pulling will be;
F - Fr = ma
Where
F = ?m = 84 kga = 1.2 m/s²N = ?μ = 0.35N = mg
N = 84 × 9.8
N = 823.2 N
Fr = μN
Fr = 0.35 × 823.2
Fr = 288.12 N
F - 288.12 = 84 × 1.2
F - 288.12 = 100.8
F = 100.8 + 288.12
F = 388.92 N
Therefore, Mr. London must be pulling with a force of 388.9 N
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of the following and draw a neat, properly labelled free body diagram. Indicate the size of forces with the lengths of the arrows. i.e., if two forces are the same size draw them the same length and if one is much bigger draw it much longer. a) The Space Shuttle accelerating vertically just after leaving the launch pad.
We will have that the diagram will be the following:
Here "F" is the force the shuttle is using to take off, friction is the friction with the air and "W" is the weight of the shuttle.
Classify the types of forces below into four groups in the table provided. Write only the letters to represent the forces. Give a heading for each group in the table.
A The force which prevents a glass bottle from slipping out of your hand
B The force which makes it difficult to climb a steep mountain
C The force which gives you weight
D The force which makes it difficult for you to push down a float in water
E The force which causes a parachutist to fall when he jumps out of a helicopter
F The force which slows down an airplane moving in air
G The force which makes a compass turns
Gravity force, friction force and buoyant force are the types of forces given below.
A) The force which prevents a glass bottle from slipping out of your hand- friction force
B) The force which makes it difficult to climb a steep mountain- gravity
C) The force which gives you weight- gravity
D) The force which makes it difficult for you to push down a float in water- buoyant force
E) The force which causes a parachutist to fall when he jumps out of a helicopter- gravity
F) The force which slows down an airplane moving in air- friction force
G) The force which makes a compass turns- gravity
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in a particle accelerator a proton moves at constant speed 0.750c in a circle of radius 663 m. what is the net force on the proton?
In a particle accelerator a proton moves at constant speed 0.750c in a circle of radius 663 m. The net force on the proton will be .0127 * [tex]10^{-11}[/tex] N
Any object moving in a circle (or along a circular path) experiences a centripetal force. That is, there is some physical force pushing or pulling the object towards the center of the circle.
Force = m ( [tex]v^{2} / R[/tex])
m= mass
v = speed
R = radius
force = 1.67 * [tex]10^{-27}[/tex] * [tex](0.75 * 3 * 10^{8}) ^{2}[/tex] / 663 = 0.0127 * [tex]10^{-11}[/tex] N
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A capacitor is constructed of two large, identical, parallel metal plates separated by a small distance d. A battery fully charges the capacitor and is then disconnected. If, instead of separating the plates, the empty space between the plates is filled with a slab of insulating material that has a dielectric constant κ= 2, which of the following correctly describes the change, if any, of the voltage across the capacitor, the electric field between the plates, and the energy stored in the capacitor? 1) Voltage halvesElectric field halves Energy halves 2. Voltage halves Electric field halves Energy does not change 3. Voltage does not change Electric field does not change Energy halves 4. Voltage does not changeElectric field halves Energy halves 5. Voltage does not change Electric field does not change Energy does not change
The capacitance of a capacitor of a parallel plate is given by:
[tex]C=\frac{kA\cdot\epsilon_o}{d}[/tex]Where:
[tex]\begin{gathered} \epsilon_o=_{\text{ }}Vacuum_{\text{ }}permittivity \\ k=_{\text{ }}Dielectric_{\text{ }}constant=2 \\ A=_{\text{ }}Area_{\text{ }}of_{\text{ }}the_{\text{ }}plates \\ d=_{\text{ }}distance_{\text{ }}betwen_{\text{ }}the_{\text{ }}plates \end{gathered}[/tex]We also know:
[tex]\begin{gathered} Q=\frac{q}{V} \\ so\colon \\ \frac{q}{V}=\frac{kA\cdot\epsilon_o}{d} \\ V=\frac{qd}{kA\cdot\epsilon_o} \\ if \\ k=2 \\ V=\frac{1}{2}(\frac{qd}{kA\cdot\epsilon_o}) \end{gathered}[/tex]As we can see the voltage halves
And since:
[tex]\begin{gathered} E=\frac{V}{d} \\ W=qV \end{gathered}[/tex]We can conclude that electric field and also the energy halve
What is the equation for finding the gravitational force of an object? (1 point)
The equation for finding the gravitational force of an object is F = mg.
option D is the correct answer.
What is gravitational force of an object?Gravitational force is an attractive force that exists between all objects with mass due to the influence of the Earth's gravitational pull.
An object with mass attracts another object with mass.
The magnitude of the force is directly proportional to the masses of the two objects and inversely proportional to the square of the distance between the two objects according to Newton's law of universal gravitation.
Mathematically, the formula for gravitational force is given as;
F = mg
where;
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Light of wavelength 589 nm in vacuum passes through a piece of fused quartz of index of refraction n = 1.458. (a) Find the speed of light in fused quartz. (b) What is the wavelength of this light in fused quartz? (c) What is the frequency of the light in fused quartz?
The speed of light in fused quartz 2.058 * [tex]10^{8}[/tex] m/s
The wavelength of the light in fused quartz 404.322 * [tex]10^{-9}[/tex] m
The frequency of the light in fused quartz 0.00509 * [tex]10^{17}[/tex] hz
refractive index of a material = speed of light in vacuum / speed of light in that medium
1.458 = 3 * [tex]10^{8}[/tex] / speed of light in that medium
speed of light in fused quartz = 3 * [tex]10^{8}[/tex] / 1.458 = 2.058 * [tex]10^{8}[/tex] m/s
frequency = c / lambda = 3 * [tex]10^{8}[/tex] / 589 * [tex]10^{-9}[/tex] = 0.00509 * [tex]10^{17}[/tex] hz
wavelength of light in fused quartz = speed of light in fused quartz / frequency
= 2.058 * [tex]10^{8}[/tex] / 0.00509 * [tex]10^{17}[/tex] = 404.322 * [tex]10^{-9}[/tex] m = 404.322 nm
wavelength = wave velocity in fused quartz / frequency
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Circuit breakers are connected in series so that the circuit will open in case of dangerously high current.TrueFalse
Circuit breakers are connected in series so that the circuit will open in case of dangerously high current.
that is True
I need help with this practice problem. Observe what happens in each of these three spheres with rain?Give at least two sentences each HYDROSPHERE:BIOSPHERE:GEOSPHERE:
The hydrosphere is the amount of water that there is on the planet. Water follows a cycle called the cycle of water where the heat from the sun evaporates water and is collected in clouds that eventually condensate and precipitates back to the surface in form of rain.
The biosphere is the part of the earth where there is life. When it rains this life receives the water and is used for various cycles that sustain life.
The geosphere is the soil of the earth. This soil receives the water and usually, this sinks in the soil sometimes accumulating and eventually evaporating again. This water is essential to sustain life.
A sample of silver at 10°C is heated to 90°C when 1 kcal of heat is added. What is the mass of the silver?
We can use the following formula:
[tex]q=m\cdot c\cdot(T2-T1)[/tex]Where:
q = heat = 1 kcal = 4184000J
c = specific heat (of silver) = 0.235 J °C /g
m = mass
T1 = Initial temperature = 10°C
T2 = Final temperature = 90°C
Therefore, solve for m:
[tex]\begin{gathered} m=\frac{q}{c(T2-T1)} \\ m=\frac{4184000}{0.235(90-10)} \\ m=222553.1915g \end{gathered}[/tex]Answer:
222553.1915g
You're standing on a ramp that is inclined at a 25 degree angle. The weight (Fg) experienced is 50N. What is the parallel force (Fx) and the perpendicular force (Fy)?I need to do the following: 1. Draw a free body diagram2.Identify Givens and Unknowns3.Identify the Equations4.Set up the equation using the givens and unknowns5.Solve
Answer:
Fx = 21.13 N
Fy = 45.32 N
Explanation:
In this case, the free body diagram is:
We can see that there is a right triangle formed by the weight (Fg) and the ramp. So, we can calculate the value of angle θ.
25 + 90 + θ = 180
115 + θ = 180
θ = 180 - 115
θ = 65
Because the sum of the interior angles of a triangle is always 180 degrees.
Now, we can calculate the parallel force and the perpendicular force using the trigonometric functions sine and cosine, so
Fx = Fg cos θ
Fy = Fg sin θ
So, replacing Fg = 50 N and θ = 65, we get:
Fx = 50 cos(65) = 21.13 N
Fy = 50 sin(65) = 45.32 N
Therefore, the answers are:
Fx = 21.13 N
Fy = 45.32 N
Viewers of Star Trek hear of an antimatter drive on the Starship Enterprise. One possibility for such a futuristic energy source is to store antimatter charged particles in a vacuum chamber, circulating in a magnetic field, and then extract them as needed. Antimatter annihilates with normal matter, producing pure energy. What strength (in T) magnetic field is needed to hold antiprotons, moving at 6.10 ✕ 107 m/s in a circular path 1.70 m in radius? Antiprotons have the same mass as protons but the opposite (negative) charge. (Enter the magnitude.)
Data:
B=?, v=6.10*10^7 m/s, R=1.70m, m=1.67*10^(-27)kg, q=-1.6*10^(-19)C
Answer:
Firstly, we need to remember the formula for the Magnetic force, which is:
[tex]F_m=|q|vB[/tex]However, in this scenario the magnetic force will act as a centripetal force, thus:
[tex]F_m=\frac{mv^2}{R}[/tex]If we equal both of them:
[tex]|q|vB=\frac{mv^2}{R}\Rightarrow B=\frac{mv}{|q|R}[/tex]Replacing our values:
[tex]B=\frac{1.67*10^{-27}*6.1*10^7}{1.6*10^{-19}*1.7}=0.3745T[/tex]Then, our magnetic field will be B=0.3745T
Two astronauts, of masses 60 kg and 80 kg, are initially right next to each other and at rest in outer space. They suddenly push each other apart. What is their separation after the heavier astronaut has moved 12 m?24 m16 m9.0 m28 m21 m
We will have the following:
First, we recall that momentum is given by:
[tex]m_1v_0+m_2v_0=m_1v_1+m_2v_2[/tex]So:
[tex]\begin{gathered} (60kg)(0m/s)+(80kg)(0m/s)=(60kg)v_1+(80kg)v_2 \\ \\ \Rightarrow v_1=\frac{-(80kg)v_2}{(60kg)}\Rightarrow v_1=-\frac{4}{3}v_2 \end{gathered}[/tex]Then:
[Let's assume that when astronaut 2 moved 12 meters = t]
[tex]\begin{gathered} x_1=v_1t\Rightarrow x_1=-\frac{4}{3}v_2t \\ \\ x_2=v_2t\Rightarrow t=\frac{12}{v_2} \end{gathered}[/tex]Then:
[tex]x_1=-\frac{4}{3}v_2\ast\frac{12}{v_2}\Rightarrow x_1=-16m[/tex]Finally, the total distance will be:
[tex]\begin{gathered} d=|x_1|+|x_2|\Rightarrow d=16m+12m \\ \\ \Rightarrow d=28m \end{gathered}[/tex]The mass of a satellite orbiting Earth is 15000 kg.
Newton's universal law of gravity
[tex]F=G\frac{m1\cdot m2}{r^2^{}}[/tex]Where:
F= force between objects
m1= mass 1 = 15,000 kg
m2= mass 2 = 6x10^24
r = distance = 34,000,000 m
G= universal contant of gravitation = 6.67 x10^-11
Replacing:
[tex]F=6.67\cdot10^{-11}\cdot\frac{15,000\cdot6x10^{24}}{(34,000,000)^2}[/tex]F= 5,193 N
Describe in simple terms each of Kepler's three laws. Why were Tycho Brahe's observations so important for Kepler to develop these laws?
Kepler's first law of planetary motion states that every planet’s orbit is elliptical and has the Sun at a focus
Kepler's second law of planetary motion states that the line joining the Sun and a planet sweeps out equal areas in equal times
Kepler's third law of planetary motion states that the square of a planet’s orbital period is proportional to the cube of the semi-major axis of its orbit
Tycho Brahe provided some accurate astronomical data which makes it possible for Kepler to develop the laws of planetary motion. He devised the best instruments available before the invention of the telescope. These data and instrument provided by Tycho Brahe was able to assist Kepler in formulating these laws
Victor is driving south. He is traveling at 12 m/s, when he enters an area with a new speed limit. Aver a period of 6 seconds, his speed increases from 12 m/s to 29 m/s. What is Victor’s acceleration during this period?
Answer:
1.1417 m/s²
Explanation:
Acceleration = final velocity - initial velocity/ time
a= [tex]\frac{v-u}{t}[/tex]
a= [tex]\frac{29-12}{12}[/tex]
a= [tex]\frac{17}{12}[/tex]
a= 1.417 m/s² or [tex]\frac{17}{12}[/tex] m/s² in fraction form
2. A Carnot engine operates between a 1500 C reservoir and a -20 C reservoir. What is the efficiency of the engine?1. 83%2. 86 %3. 99 %4. 1.3 %
The efficiency of a Carnot engine is given by
[tex]\eta=1-\frac{T_C}{T_H}[/tex]Where TC is the temperature of the cold source in kelvin and TH is the temperature of the hot source in kelvin.
Let us first convert the given temperatures from celsius to kelvin.
[tex]\begin{gathered} T_C=-20+273=253K \\ T_H=1500+273=1773K \end{gathered}[/tex]So, the efficiency is
[tex]\begin{gathered} \eta=1-\frac{253}{1773} \\ \eta=0.857 \\ \eta=85.7\% \end{gathered}[/tex]Rounding off to a whole number
[tex]\eta=86\%[/tex]Therefore, the efficiency of the engine is 86%
A bicycle wheel, of radius 0.300 m and mass 2.07 kg (concentrated on the rim), is rotating at 4.00 rev/s. After 59.0 s the wheel comes to a stop because of friction. What is the magnitude of the average torque due to frictional forces?
ANSWER:
0.079 J
STEP-BY-STEP EXPLANATION:
The average torque exerted due to friction force is:
[tex]\tau=I\alpha[/tex]Here, I is the moment of inertia and α is the angular acceleration.
The mass of wheel is concentrated at the rim. Therefore, the moment of inertia of wheel is,
[tex]I=m\cdot r^2[/tex]Here, m is the mass of wheel and r is the radius of wheel.
replacing:
[tex]\begin{gathered} I=2.07\cdot0.3^2 \\ I=0.1863\text{ kg}\cdot s^2 \end{gathered}[/tex]The angular speed is decreased from 4 rev/s to 0 rev/s in 59 sec. Therefore, the angular acceleration is calculated as:
[tex]\begin{gathered} \alpha=\frac{0-4}{59} \\ \alpha=0.068\cdot\frac{rev}{\sec}\cdot\frac{2\pi\text{ rad/rev}}{1rev/sec^2} \\ \alpha=-0.426rad/sec^2 \end{gathered}[/tex]The negative sign represents that the wheel is de-accelerating.
Replacing:
[tex]\begin{gathered} \tau=I\alpha \\ \tau=0.1863\cdot-0.426 \\ \tau=-0.079\text{J} \end{gathered}[/tex]The negative sign represents the direction of torque i.e. clockwise direction. Thus, the magnitude of average torque is 0.079 J.
the position of an object is given by: x(t)=2t^3-35t^2+10 what is the acceleration of the object at t=250 seconds?
We are given that a particle's position is determined by the function:
[tex]x\left(t\right)=2t^3-35t^2+10[/tex]We are asked to determine the acceleration of the object. To do that we will first determine the first derivative of the position with respect to time, i. e. the velocity of the particle:
[tex]\frac{dx}{dt}=\frac{d}{dt}(2t^3-35t^2+10)[/tex]Now, we distribute the derivative operator:
[tex]\frac{dx}{dt}=\frac{d}{dt}(2t^3)-\frac{d}{dt}(35t^2)+\frac{d}{dt}(10)[/tex]Now, we use the following rule to determine each derivative:
[tex][/tex]A spaceship travels at an enormous speed to go from one star system to another. As it reaches its destination, its “hyperdrive” deactivates, bringing the ship to an immediate halt in orbit around a planet.
Why does this defy physics? Give Equations/ Laws to justify yourself
This situation defies the laws of physics because it has no physical basis to explain the immediate stoppage of the ship.
Why does this situation defy physics?This situation defies the laws of physics because it describes an event in which an ship stops abruptly without any apparent physical explanation.
From the above, it can be inferred that this does not have scientific support. Additionally, it is defying the laws of physics because, according to Newton's second law, every body in motion continues to move at a constant speed. Therefore, if the ship goes to a hypervelocity it must continue moving, by Newton's second law. Additionally, if there were a force such as friction or gravity that causes it to stop, this would not be immediately but progressively.
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An acorn is dropped and reaches the ground in 2.0s. What is the acorn’s velocity just as it hits the ground? How high above the ground was it released?
Take into account that the vertical distance traveled by the acorn can be calculated by using:
[tex]h=\frac{1}{2}gt^2[/tex]where,
g: gravitational acceleration constant = 9.8m/s^2
t: time acorn takes to hit the ground = 2.0s
h: height at which acorn is initially = ?
Replace the given values of the parameters into the previous formula and simplfiy:
[tex]h=\frac{1}{2}(9.8\frac{m}{s^2})(2.0s)^2=19.6m[/tex]Hence, the acorn was released from a high of 19.6m above the ground.
The velocity just after acorn hits the ground is given by:
[tex]\begin{gathered} v=gt \\ v=(9.8\frac{m}{s^2})(2.0s)=19.6\frac{m}{s} \end{gathered}[/tex]Hence, the speed is 19.6 m/s
Write a rule for the sequence. 3, -3, -9, -15. A. Start with 3 and add -6 repeatedly B. Start with -6 and add 3 repeatedly C. Start with 3 and 6 repeatedly D. Start with 3 and subtract -6 repeatedly
Substract two consecutive terms of the sequence to see if there is a common difference:
[tex]\begin{gathered} (-3)-(3)=-3-3=-6 \\ (-9)-(-3)=-9+3=-6 \\ (-15)-(-9)=-15+9=-6 \end{gathered}[/tex]As we can see, there is a common difference of -6.
Then, if a number of the sequence is given, the next one can be found by adding -6 (which is the same as subtracting 6).
Notice that the first term of the sequence is 3.
Then, the rule for the sequence is to start with 3 and add -6 repeatedly.
Therefore, the correct choice is option A) Start with 3 and add -6 repeatedly.