Answer: This is an evolutionary adaption
Explanation:
As a result, practically all the heat you receive from a campfire when you are sitting next to one is transmitted through thermal radiation. Because of this, the side of your body that is facing the fire warms up, while the side that is facing away from it remains cool.
What our fingers wide open while sitting in a heater?Since all the hot air is rising, you can actually fit your hand through the flame's base, which is also where the cold air from the surrounding space is drawn in. The flame's base is extremely chilly. You may reach through it and touch it with some soot.
Therefore, Heat is transferred through convection, which is the large-scale movement of molecules in fluids like liquid and gas. Consequently, one becomes warm while seated close to a fire.
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what is the final velocity (magnitude and direction) of a 100-kg rugby player who is initially running at 8.00 m/s east but collides head-on with a padded goal post and experiences a backward force of 1.8 x104 n for 0.05 second.
The final velocity of a 100-kg rugby player which collides head-on with a padded goal post is 53 m/s.
The change in momentum (p) over the change in time (t) equals force (F).
then,
F = [tex]\Delta\\[/tex]p / t
[tex]\Delta\\[/tex]p = F x t
[tex]\Delta p = F_{net} t \\\Delta p = mv' - mv\\mv' - mv= F_{net} t \\mv' = mv + F_{net} t[/tex]
m = 100kg
v = 8 m/s
F = 0.9 x 10⁴ N
t = 0.5 second
using these values in above equation we can calculate final velocity as :
100v' = 0.9 x 10⁴x 0.5 + 100 x 8
100v' = 4500 + 800
100v' = 5300
v' = 5300/100
100v' = 53 m/s.
The final velocity of a 100-kg rugby player which collides head-on with a padded goal post is 53 m/s.
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a 150. g baseball is thrown with a speed of 20. m/s. it is hit straight back toward the pitcher at a speed of 40 m/s. if the baseball and bat are in contact for 6.0 ms, what is the magnitude of the average force delivered to the ball?
If the baseball that is thrown with a speed of 20 m / s and bat are in contact for 6.0 m s, the magnitude of the average force delivered to the ball of mass 150 g is 0.5 KN
a = v / t
a = Acceleration
v = Velocity
t = Time
v = 20 m / s
t = 6 m s
t = 6 * [tex]10^{-3}[/tex] s
a = 20 / 6 * [tex]10^{-3}[/tex]
a = 3.3333 * 10³ m / s²
According to Newton's second law of motion,
F = m a
F = Force
m = Mass
m = 150 g
m = 0.15 kg
F = 0.15 * 3.3333 * 10³
F = 0.5 * 10³ N
F = 0.5 KN
Therefore, the magnitude of the average force delivered to the ball is 0.5 KN
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A ball is dropped from a hot air balloon at a height of 425 m and falls straight to the ground.
Determine the height above ground, the velocity and the acceleration of the ball after it has fallen
for 2.00 s.
The velocity and the acceleration of the ball after it has fallen
for 2.00 s 9.8 m/s.
Calculation:-
S = ut + 1/2 at²
= 0 + 0.5 × 9.8 (2)²
= 4.9 × 4
= 19.6 m
v² = u² + 2aS
v² = 0 +2×9.8 × 19.6
v = √96.04 m
= 9.8 m/s
Acceleration is the rate of change of the velocity of an item with appreciation to time. Accelerations are vector portions. The orientation of an item's acceleration is given by the orientation of the net pressure appearing on that object.
Acceleration is the charge at which velocity modifications with time, in terms of each speed and route. A factor or an object moving in a straight line is accelerated if it quickens or slows down. movement on a circle is extended despite the fact that the rate is consistent because the course is continually changing.
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What happens to light waves from a star as the star moves toward Earth?A. They appear to shift toward red.B. They appear to shift toward blue.C. They appear to become mechanical waves.D. They appear to stop.
When a star moves toward or away from the earth, the light will be in a slightly different place in the spectrum from where a start would be at rest.
Due to the doppler effect, if a star moves toward the earth, the star's spectral lines will make a shift toward the blue end of the spectrum.
Therefore, the light waves from a star as the star moves toward the earth will appear to shift toward blue.
ANSWER:
B. They appear to shift toward blue.
Now that you have your research, you must write 6-8 sentence summary of how Newton’s Laws, energy, and forces are seen/used on roller coasters. You must use the vocabulary words above in your explanation. Bold and/or underline the vocabulary words in your writing. (PLEASE I NEED THIS) 0o0000
Based on Newton's first law of motion, the roller coaster will continue its motion in a straight line unless and external force (the break) acts on it.
In accordance with the law of conservation of energy, as the roller coaster moves from the top position to the lower position, its potential energy will be converted to kinetic energy.
What is Newton's first law of motion?
Newton's first law of motion states that an object at rest or uniform motion in a straight line will continue in that path unless acted upon by an external force.
Based on Newton's first law of motion, the roller coaster will continue its motion in a straight line unless and external force (the break) acts on it.
The law of conservation of energy states that energy can neither be created nor destroyed but can be converted from one form to another.
Based on the law of conservation of energy, as the roller coaster moves from the top position to the lower position, its potential energy will be converted to kinetic energy.
The potential energy of the roller coaster is maximum at the highest position while the kinetic energy is maximum at the lowest position.
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What was the impact of the caravel, astrolabe, and magnetic compass on sea navigation?.
Astrolabe by measuring the sun's angles, this tool allowed sailors to determine their latitude, or where they were in relation to the equator of the planet. By keeping an eye on where the sun is in the sky, an astrolabe can also be used to tell time.
What does a magnetic compass do?A magnetic compass is a tool used in surveying or navigation that uses a magnetic pointer that is aligned with the Earth's magnetic field to determine direction on the surface of the planet.
The north-south axis is the alignment point for magnets because of how powerful a magnet the Earth is. The Earth's rotational axis and the magnetic field's poles roughly line up. This indicates that the north geographic pole, also known as true north, and the north magnetic pole are nearly parallel. A light magnet that is free to move will align itself north-south. On the other hand, gravity and friction will prevent a heavy bar magnet from moving when it is placed on a tabletop.
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two coils are wound around the same cylindrical form, like the coils in example 30.1. when the current in the first coil is decreasing at a rate of -0.242 a>s, the induced emf in the second coil has magnitude 1.65 * 10-3 v. (a) what is the mutual inductance of the pair of coils? (b) if the second coil has 25 turns, what is the flux through each turn when the current in the first coil equals 1.20 a? (c) if the current in the second coil increases at a rate of 0.360 a>s, what is the magnitude of the induced emf in the first coil?
(a) Mutual inductance = 6.818 × 10⁻³ Hz
(b) Total flux = 3.27 × 10⁻⁴ Wb
(c) Induced EMF = 2.45 × 10⁻³ V
What is induced EMF?When the bar magnet is pushed out, an electromotive force is induced in the coil. An EMF of opposite sign is produced by moving in the opposite direction, and the EMF is also flipped by reversing the poles. You can get the same result by moving the coil instead of the magnet - relative motion is important.
For mutual inductance:
M = ∈/(Δi/Δ)
Where, M = mutual inductance
∈ = 1.65 × 10⁻³ V
Δi/Δt = -0.242 A/s
M = 1.65 × 10⁻³/ -0.242
M = 6.818 × 10⁻³ Hz or 6.818 mHz
For the calculation of the flux through each turn:
∅ = MI/N
Where, ∅ = Total flux
M = Mutual inductance
I = Current through one coil
N = Number of turns
∅ = (6.818 × 10⁻³ × 1.20)/25
∅ = 3.27 × 10⁻⁴ Wb
For induced EMF:
∈ = M × (Δi/Δt)
∈ = induced EMF
M = 6.818 × 10⁻³ Hz
Δi/Δt = 0.360 A/s
∈ = 6.818 × 10⁻³ × 0.360
∈ = 2.45 × 10⁻³ V
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An airplane is sitting standstill on a runway and it is exerting -230,000N onto the ground. What is the mass of the plane?
Answer: Force = mass x acceleration
Explanation: Here, the plane is standing still so acceleration here is
acceleration due to gravity ( 9.8 m/[tex]s^{2}[/tex]) So,
Force = mass x 9.8
230000 = mass x 9.8
Mass = [tex]\frac{230000}{9.8}[/tex] = 23,469.39 kgs
Here force is negative because it is acting against gravity. Also, since the unit of force is Newton so the unit of mass is in kgs
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Background:
Imagine being in an elevator and riding from the 1st floor to 20th floor. You start from
rest, speed up (maybe for a floor or two) until you get up to cruising speed. Then you
cruise for several floors until you are nearing your destination. As you near your
destination, you slow down from cruising speed to a final stopping position (i.e., a zero
speed). What would you feel during this time and why would you feel it?
A person feels lighter than his Normal weight when the lift is accelerating downwards.
The price at which an object adjustments its velocity is referred to as acceleration, a vector variable. If an item's velocity is changing, it's miles accelerating. A moving object can every so often adjust its velocity by the same amount every 2nd. a transferring item that adjustments its speed with the aid of 10 m/s per second. since the pace is changing through a set quantity each second,
that is called a regular acceleration. it's miles important to differentiate among an item with a steady acceleration and one with a constant velocity. Be not deceived! An object is accelerating if its speed is changing, whether or not with the aid of a hard and fast amount or a variable quantity. additionally, a transferring item with a regular pace isn't always accelerating.
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You swing a weight attached to a string in a vertical circle. at the top of the circle the string just barely goes slack for an instant. part a choose the correct statement for the the centripetal acceleration of the weight.
If the ball isn't travelling as swiftly as the force is pushing itself to keep it moving (in a circular motion), it will fall because gravity and tension pull downward at the top of the swing.
Speed is calculated using the distance travelled and the time needed to cover that distance. Speed is a scalar number because it just has a vector and no magnitude.You can determine something's average speed if you know how far it has travelled and how long it took to get there. One can determine speed by simply dividing by the amount of time. Stride length and cadence both affect running pace. The stride cadence is the frequency of steps taken per second, and the stride length is the distance covered by each step. Combining these factors yields a precise mathematical description of running.To know more about force
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What power is emitted by a circuit with a 9.00 volt battery and a 50.0 Ohm resistor? A)450 W B)0.00222 W C)1.62 W D)5.55 W E)0.180 W
Given,
Voltage, V=9 V
Resistor, R=50.0 ohm
To find
The power emitted by the battery.
Explanation
The power is:
[tex]\begin{gathered} P=\frac{V^2}{R} \\ \Rightarrow P=\frac{9^2}{50} \\ \Rightarrow P=1.62\text{ W} \end{gathered}[/tex]Conclusion
The power is: C.1.62W
The speed of a car is decreased uniformly from 30. meters per second to 10. meters per second in 4.0 seconds.
Answer: The car slows down by 10 meters per second every second.
Explanation:
AnswerThe speed of a car is decreased uniformly from 30. meters per second to 10. meters per second in 4.0 seconds. What was the car's acceleration ?
We have the following data:
V (final velocity) = 10 m/s
Vo (initial velocity) = 30 m/s
ΔV (speed interval) = V - Vo → ΔV = 10 - 30 → ΔV = - 20 m/s
ΔT (time interval) = 4.0 seconds
a (average acceleration) = ? (in m/s²)
Explanation:
Alisha & Ariana are in a car (523.5 kg) sitting in a driveway. Ariana distracts Alisha and before she knows it she is going to hit the garage door. She tries to brake and stop the car. The coefficient of friction between the tires and the road is 0.69. Unfortunately, it’s too late and she drives the car straight into her parent’s garage door with a rightward force of 6,366 N What is the frictional force that the car experiences?
The frictional force that the car experiences is 3,553.43 N.
What is the frictional force experienced by the car?
The frictional force that the car experiences is calculated by applying Newton's second law of motion as follows;
Mathematically, the formula for frictional force is given as;
Ff = μFn
where;
μ is the coefficient of frictionFn is the normal force of the objectFf is the frictional forceFf = μmg
where;
m is the mass of the carg is acceleration due to gravityThe given parameters;
the mass of the car, m = 525.5 kg
the coefficient of friction = 0.69
Substitute the given parameters and solve for the frictional force that the car experiences as it moves along the parent's garage.
Ff = 0.69 x 525.5 x 9.8
Ff = 3,553.43 N
Thus, the frictional force that the car experiences depends on the mass of the car and coefficient of friction.
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A 25N force is acting on a body moving on a straight line with Initial momentum 20 kam's. Find the final momentum after 4 seconds. (Fxt=Pr-Pi)
The final momentum of the body is equal to 120 Kg.m/s.
What is momentum?Momentum can be described as the multiplication of the mass and velocity of an object. Momentum is a vector quantity as it carries magnitude and direction.
If m is an object's mass and v is its velocity then the object's momentum p is: [tex]{\displaystyle \mathbf {p} =m\mathbf {v}[/tex] . The S.I. unit of measurement of momentum is kg⋅m/s, which is equivalent to the N.s.
Given the initial momentum of the body = Pi = 20 Kg.m/s
The force acting on the body, Pf = 25 N
The time, Δt = 4-0 = 4s
The Force is equal to the change in momentum: F ×Δt = ΔP
25 × 4 = P - 20
100 = P - 20
P = 100 + 20 = 120 Kg.m/s
Therefore, the final momentum of a body is 120 Kg.m/s.
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what is an advantage of concentrating solar energy as compared to other solar technologies? choose the best answer.
CSP technologies can be used to generate electricity by converting sunlight energy to power a turbine, but the same basic technologies can also be used to deliver heat to a variety of industrial applications such as water desalination, enhanced oil recovery, food processing, chemical production, and mineral processing.
What is concentrating solar-thermal power (CSP) technology and how does it work?Concentrating solar-thermal powertechnologies use mirrors to reflect and concentrate sunlight onto a receiver. The energy from the concentrated sunlight heats a high temperature fluid in the receiver.
This heat, also known as thermal energy, can be used to spin a turbine or power an engine, thereby producing electricity. It can also be used in industrial applications such as water desalination, improved oil recovery, food processing, chemical production, and mineral processing.
Utility-scale projects typically employ concentrated solar-thermal power systems. Utility-scale CSP plants can be configured in a variety of ways. Mirrors are arranged around a central tower that serves as the receiver in power tower systems. Linear systems use rows of mirrors to focus sunlight onto parallel tube receivers located above them.
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The Jamaican bobsled team hit the brakes on their sled so that it decelerates at
a
uniform rate of 0.43 m/s?. How long does it take to stop if it travels 85 m before
coming to rest?
the answer is in the photo
hopes it help!
A rock is thrown horizontally from the top of a 494.9 m high cliff on Earth near sea level with an initial velocity of 27.6. The ground below the cliff is level. How long, in seconds, will it take the rock to hit the ground below the cliff? Enter your answer at least to the nearest tenth of a second, but do not include units in your answer.
Answer:
Time 10.0 s
Explanation:
Given:
H = 494.9 m
V = 27.6 m/s
g = 9.8 m/s²
___________
t - ?
The fall time is found from the formula:
H = g·t² / 2
t = √ (2·H / g) = √ (2·494.9 / 9.8 ) ≈ 10.0 s
Attention! An extra given is speed. Find the distance from the base of the rock to the point where the stone fell:
L = V·t = 27.6·10.0 = 276 m
2 poin6. What is the speed of an earthquake wave if it has a wavelength of2300 m and a frequency of 3 Hz? *6900 m/s5300 m/s6000 m/s1300 m/s
Given that the wavelength of the wave is
[tex]\lambda=2300\text{ m}[/tex]The frequency of the wave is f = 3 Hz
We have to find the speed of the wave.
Let the speed of the wave is v.
The speed can be calculated by the formula,
[tex]v=f\lambda[/tex]Substituting the values, the speed of the wave will be
[tex]\begin{gathered} v=\text{ 3}\times2300 \\ =6900\text{ m/s} \end{gathered}[/tex]Thus, the speed of the wave is 6900 m/s.
The maximum speed with which a 1700 kg horse makes a 180-degree turn is 12 m/s. The radius of the circle through
which the horse is turning is 30 meters. Determine the force of friction acting on the horse as it makes this turn.
a. 20400 N
b. 13981.94 N
c. 680 N
d. 8160 N
When making a 180-degree turn with a radius of 15 meters, a 900 kg car experiences a coefficient of friction of 0.60
a container holds a gas consisting of 1.50 moles of oxygen molecules. One in a million of these molecules has lost a single electron. What is the net charge of the gas?
A container holds a gas consisting of 1.50 moles of oxygen molecules. One in a million of these molecules has lost a single electron. the net charge of the gas will be + 9.033 * [tex]10^{17}[/tex]
If a negative charge is lost by an atom , then due to conservation of charge , that atom will acquire a positive charge . Similarly , if positive charge is lost then that atom will acquire a negative charge .Now in above question
Total number of moles = 1.5
number of molecules in 1.5 moles of oxygen = 1.5 * 6.022 *[tex]10^{23}[/tex] = 9.033 *[tex]10^{23}[/tex] molecules
9.033 *[tex]10^{23}[/tex] / [tex]10^{6}[/tex] million molecules = 9.033 * [tex]10^{17}[/tex] million molecule
1 in a million has lost a single electron
9.033 * [tex]10^{17}[/tex] million molecule will loose 9.033 * [tex]10^{17}[/tex] electron
the net charge of the gas will be + 9.033 * [tex]10^{17}[/tex]
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A coin rolls off the edge of a table. The coin was traveling with a speed of
0.40 m/s. It lands 0.20 m away from the edge of the table. How high is the table?
(Hint: You must solve for time before you can solve for d)
Answer:
Approximately [tex]1.3\; {\rm m}[/tex] (assuming that [tex]g = 9.81\; {\rm m\cdot s^{-2}}[/tex], the table is level, and that air resistance on the coin is negligible.)
Explanation:
Assume that the air resistance on the coin is negligible. As long as the coin is in the air, its horizontal velocity of the coin will be constantly equal to the original value, [tex]v_{x} = 0.40\; {\rm m\cdot s^{-1}}[/tex].
It is given that the horizontal displacement of this coin is [tex]x_{x} = 0.20\; {\rm m}[/tex] during the flight. Divide this horizontal displacement by horizontal velocity to find the duration [tex]t[/tex] of the flight:
[tex]\begin{aligned} t &= \frac{x_{x}}{v_{x}} \\ &= \frac{0.20\; {\rm m}}{0.40\; {\rm m\cdot s^{-1}}} \\ &= 0.50\; {\rm s}\end{aligned}[/tex].
Also because air resistance on the coin is negligible, the vertical acceleration of the coin will be constantly [tex]a_{y} = (-g) = (-9.81)\; {\rm m\cdot s^{-2}}[/tex]. If the table is level, the initial vertical velocity of the coin [tex]u_{y}[/tex] will be [tex]0\; {\rm m\cdot s^{-1}}[/tex]. Apply the SUVAT equation [tex]x = (1/2)\, a\, t^{2} + u\, t[/tex] to find the vertical displacement of the coin during the [tex]t = 0.5\; {\rm s}[/tex] that it is in the air:
[tex]\begin{aligned}x_{y} &= \frac{1}{2}\, a_{y}\, t^{2} + u_{y}\, t \\ &= \frac{1}{2} \, (-9.81\; {\rm m\cdot s^{-2}})\, (0.5\; {\rm s})^{2} + (0\; {\rm m\cdot s^{-1}})\, (0.50\; {\rm s}) \\ &\approx (-1.3)\; {\rm m}\end{aligned}[/tex].
In other words, the coin lands approximately [tex]1.3\; {\rm m}[/tex] below the table edge. Hence, the height of the table would be approximately [tex]1.3\; {\rm m}\![/tex].
A rock is thrown upwards at a 90o angle with a velocity of 15.8. What is the total hang time of the rock?
Answer:
Below
Explanation:
When ball reaches max height its velocity = 0 and it is 1/2 of the way through its roundtrip
vf = vo + at
0 = 15.8 - 9.81 t shows t = 1.61 s
for the roundtrip 2 x 1.61 = 3.22 s
Which of the following is NOT a means to determine the efficiency of a machine? A) useful work output/work input B) useful power output/power input C) effort x distance moved by effort/load distance moved by load D) load x distance moved by load/effort x distance moved by effort
In general terms, efficiency is output/input.
For a lever, the effort is the input and load is the output.
Thus, option C is not a means to determine efficiency as effort is the input and load is the output.
A tsunami can travel over 970 kilometers in an hour. If it’s been 3 hours since the tsunami was created, how far has it traveled?
Answer:
2910
Explanation:
970 × 3. 970 in one hour × 3 hrs. 2910 kilometers
a car headlight and an interior dome light use the same voltage, but the headlight consumes much more power because
The lights on and in your vehicle can be as important to your and your passengers' safety as seatbelts, and as visually appealing as great rims or an unusual paint color.
Why headlight consumes much more power than interior dome light ?Automobiles have been around for nearly a decade, almost as long as mass-marketable light bulbs. The first light bulbs were incandescent, which simply passed any current, AC or DC, through a high-impedance filament, which heated up, glowed, and emitted light.
Although their efficiency is low (as low as 10%), they emit light in all directions and are inexpensive. Under the heat required to generate light, the filament material (typically tungsten) evaporates and tends to collect on the inside of the glass bulb, darkening it over time.
Consumers are looking beyond incandescent lights to high intensity discharge headlights and other 12v LED lighting solutions as the automotive industry grows, but there are even more options and modifications available. While there are amazing new technologies available, not all of them are true advancements or even road-legal. Let us shed some light on the situation.
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HELP ASAP!
A train with mass of 3.1x104 kg is pushed by an engine with a force of 5.0x104N for a distance of 450.0 meters in 3.5 minutes.
How much work was done on the train? ________________J
What was the Power exerted by the train? ________________W
Work was done on the train 225x10⁵ J
Power exerted by the train 1.07 x 10⁵ W
Explain work and power?Work is the amount of energy transferred to an object when it is moved a certain distance by an external force. Since work is defined as the amount of energy (transferred), it has units of energy, and work usually has units of J (joules). The equation describing the work (W) done on a body moving a distance (s) while a force (F) is acting on it in the same direction as its motion is given by:
W = F × s
Where,
W = work done
F = force applied
s = displacement
We can define force as the rate of work. It is work done in a unit of time. The SI unit for power is the watt (W), which is the joule per second (J/s). The formula for power is:
P = W / t
Where,
P = Power
W = work done
t = time taken
Now for the given question:
W = F × s
F = 5.0x10⁴ N
s = 450.0 meters
W = 5.0x10⁴ x 450.0
W = 225x10⁵J
P = W / t
P = [tex]\frac{225}{210}[/tex] x10⁵
P =1.07 x 10⁵ W
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two solenoids, a and b, have the same length and cross-sectional area. solenoid b has three times the number of turns per unit length. what is the ratio of the self-inductance of solenoid b to that of solenoid a?
The ratio of the self-inductance of solenoid b to that of solenoid a, is 3.
Self-inductance is the property of the current-carrying coil that resists or opposes the change of current flowing through it. This occurs mainly due to the self-induced emf produced in the coil itself.
Induced emf = N A ( db/dt )
where N is the number of turns in the coil
A is the cross sectional area of the coil
db/dt is the rate of change of the magnetic field
from question we have, Nb = 3Na
Ea = Na x A x (db/dt) ......(1)
and Eb = Nb x A x (db/dt) ..........(2)
dividing both equation 1 and equation 2, we get
Eb/Ea = Nb/Na
Eb/Ea = 3Na/Na
Eb/Ea = 3
Hence The ratio of the self-inductance of solenoid b to that of solenoid a, is 3.
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Rachel has three different samples of rare Earth metals. The first sample has a mass of 5.5∗10−3 grams, the second has a mass of 1.4 grams, and the third has a mass of 4.4∗10−2 grams. Ignoring significant figures, what is the sum of these three masses?11.3∗10^−5 g1.4495g1.4495∗10^−5 g11.3 g
Because each mass has the same units we can sum them
[tex]m_t=5.5\times10^{-3}+1.4+4.4\times10^{-2}[/tex][tex]m_t=1.4495g[/tex]The sum of the 3 masses is 1.4495g
The Millennium Force Roller Coaster at Cedar Park has a hill height of 94 m and reaches a speed of 36 m/s at the bottom of the hill if the roller coaster car starts at rest. Using a mass of 120 kg for one car again, how much energy is lost to friction and heat?
The energy lost due to friction and heat is 32784 Joule.
Given parameters:
Mass of the car; M = 120 kg.
speed of the car at bottom; v = 36 m/s.
Height of the hill; h = 94 m.
Then, Gain of Kinetic energy of the car = 1/2× mass × speed²
= 1/2×120×36² Joule
= 77760 Joule.
Loss of potential energy of the car = mass× acceleration due to gravity × height
= 120 × 9.8 × 94
= 110544 Joule.
Energy lost due to friction and heat = Loss of potential energy of the car - Gain of Kinetic energy of the car
= 110544 Joule - 77760 Joule.
= 32784 Joule.
Hence, energy lost due to friction and heat is 32784 Joule.
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A projectile is launched from ground level with an initial velocity of v0 feet per second. Neglecting air resistance, it’s height in feet t seconds after launch is given by s= -16t^2+v0t. Find the time(s) that the projectile will (a) reach a height of 272 ft and (b) return to the ground when v0 is 32 feet per second
We know that the inital velity for this motion is 32 ft/s, this means that the height is given by:
[tex]s=-16t^2+32t[/tex]a)
To determine at what time the projectile will reach 272 we plug s=272 in the equation above and solve for t:
[tex]\begin{gathered} -16t^2+32t=272 \\ 16t^2-32t+272=0 \\ t^2-2t+17=0 \\ \text{ then} \\ t=\frac{-(-2)\pm\sqrt[]{(-2)^2-4(1)(17)}}{2(1)} \\ t=\frac{2\pm\sqrt[]{-64}}{2} \end{gathered}[/tex]since the discrimant of the equation is negative this means that the equation does not have real solutions.
This means that the projectile does not reach that height.
b)
To find at what time the projectile return to the ground we equate the expression for the height to zero and solve for t:
[tex]\begin{gathered} -16t^2+32t=0 \\ t(-16t+32)=0 \\ \text{then} \\ t=0 \\ or \\ -16t+32=0 \\ 16t=32 \\ t=\frac{32}{16} \\ t=2 \end{gathered}[/tex]Therefore it takes 2 seconds for the projectile to return to the ground