1.
The two measurements necessary for calculating average speed are
Correct Answer
C. Distance and time
Explanation
The average speed is calculated by dividing the total distance traveled by the time taken to travel that distance. Therefore, the two measurements necessary for calculating average speed are distance and time.
2.
A horse gallops a distance of 10 kilometers in a time of 30 minutes. Its average speed is
Correct Answer
B. 20 km/h
Explanation
The average speed of an object is calculated by dividing the total distance traveled by the time taken. In this case, the horse galloped a distance of 10 kilometers in a time of 30 minutes. To convert the time to hours, we divide by 60 (30 minutes = 0.5 hours). Therefore, the average speed is 10 km / 0.5 hours = 20 km/h.
3.
A car maintains a constant velocity of 100 km/hr for 10 seconds. During this interval its acceleration is
Correct Answer
A. Zero
Explanation
Since the car maintains a constant velocity of 100 km/hr for 10 seconds, it means that there is no change in its velocity over time. Acceleration is defined as the rate of change of velocity, so if there is no change in velocity, the acceleration must be zero.
4.
While an object near the Earth's surface is in free fall, its
Correct Answer
A. Velocity increases
Explanation
When an object near the Earth's surface is in free fall, it experiences a constant acceleration due to gravity. As time goes on, the object's velocity increases because the acceleration causes it to speed up. This is because the force of gravity is constantly pulling the object downward, causing it to gain speed as it falls. Therefore, the correct answer is that the velocity increases.
5.
A hockey puck is set in motion across a frozen pond. If ice friction and air resistance are neglected, the force required to keep the puck sliding at constant velocity is
Correct Answer
A. Zero
Explanation
If ice friction and air resistance are neglected, there are no external forces acting on the hockey puck once it is set in motion. According to Newton's first law of motion, an object will continue to move at a constant velocity unless acted upon by an external force. Therefore, no force is required to keep the puck sliding at a constant velocity.
6.
An object at rest near the surface of a distant planet starts to fall freely. If the acceleration there is twice that of the Earth, its speed one second later would be
Correct Answer
B. 20 m/s
Explanation
If the acceleration on the distant planet is twice that of Earth, it means that the object will experience a greater force pulling it down. According to the equations of motion, the speed of a freely falling object increases at a constant rate. In one second, the object's speed would be equal to the acceleration multiplied by the time, which is 2 * 1 = 2 m/s. Therefore, the object's speed one second later would be 2 m/s, which corresponds to the answer 20 m/s.
7.
If an object falling freely were somehow equipped with an odometer to measure the distance it travels, then the amount of distance it travels each succeeding second would be
Correct Answer
C. Greater than the second before
Explanation
The distance traveled by an object falling freely would be greater than the second before because the object is accelerating due to the force of gravity. As time progresses, the object's velocity increases, causing it to cover a greater distance in each subsequent second. This is in accordance with the laws of motion and gravity.
8.
If a freely falling object were somehow equipped with a speedometer, its speed reading would increase each second by about
Correct Answer
B. 10 m/s
Explanation
The correct answer is 10 m/s. When a freely falling object is equipped with a speedometer, its speed reading would increase by about 10 m/s each second. This is because objects in free fall experience a constant acceleration due to gravity, which is approximately 9.8 m/s^2. Therefore, the speed of the object would increase by 9.8 m/s every second. Rounded to the nearest whole number, this would be approximately 10 m/s.
9.
If a freely falling object were somehow equipped with a speedometer on a planet where the acceleration due to gravity is 20 m/s/s, then its speed reading would increase each second by
Correct Answer
B. 20 m/s
Explanation
On a planet where the acceleration due to gravity is 20 m/s/s, the speed of a freely falling object would increase by 20 m/s every second. This is because the acceleration due to gravity determines how quickly an object's speed changes over time. In this case, the acceleration is constant at 20 m/s/s, so the speed reading would increase by 20 m/s each second. The initial speed of the object does not affect the rate at which its speed increases, so the correct answer is 20 m/s.
10.
Twelve seconds after starting from rest, an object falling freely will have a speed of
Correct Answer
D. More than 100 m/s
Explanation
According to the laws of physics, an object falling freely under the influence of gravity will continuously accelerate. The acceleration due to gravity is approximately 9.8 m/s². Therefore, after twelve seconds, the object would have been accelerating for a significant amount of time, resulting in a speed greater than 100 m/s.
11.
If an object moves with constant acceleration, its velocity must
Correct Answer
B. Change by the same amount each second
Explanation
If an object moves with constant acceleration, its velocity must change by the same amount each second. This is because acceleration is defined as the rate of change of velocity. If the acceleration is constant, it means that the object's velocity is changing at a constant rate. Therefore, the change in velocity will be the same for each unit of time, in this case, each second.
12.
If a car increases its velocity from zero to 60 km/h in 10 seconds, its acceleration is
Correct Answer
B. 6 km/h/s
Explanation
The acceleration of a car can be calculated by dividing the change in velocity by the time taken. In this case, the car increases its velocity from zero to 60 km/h in 10 seconds. The change in velocity is 60 km/h - 0 km/h = 60 km/h. Dividing this by the time taken, 10 seconds, we get an acceleration of 6 km/h/s.
13.
If a rocket initially at rest accelerates at a rate of 50 m/s2 for one minute, its speed will be
Correct Answer
C. 3000 m/s
Explanation
The acceleration of the rocket is given as 50 m/s^2. This means that every second, the rocket's speed increases by 50 m/s. Since the rocket accelerates for one minute, which is equal to 60 seconds, the total increase in speed would be 50 m/s * 60 s = 3000 m/s. Therefore, the speed of the rocket after one minute would be 3000 m/s.
14.
An apple falls from a tree and hits the ground 5 meters below. It hits the ground with a speed of about
Correct Answer
B. 10 m/s
Explanation
When an apple falls from a tree, it accelerates due to the force of gravity. The acceleration due to gravity is approximately 9.8 m/s². Using the equation v² = u² + 2as, where v is the final velocity, u is the initial velocity (which is 0 in this case), a is the acceleration, and s is the distance fallen, we can calculate the final velocity. Plugging in the values, we get v² = 0 + 2 * 9.8 * 5, which simplifies to v² = 98. Solving for v, we find that the final velocity is approximately 9.9 m/s. Since the question asks for an estimate, the closest option is 10 m/s.
15.
It takes 6 seconds for a stone to fall to the bottom of a mine shaft. How deep is the shaft?
Correct Answer
C. About 180 m
Explanation
Based on the given information, we know that it takes 6 seconds for the stone to fall to the bottom of the mine shaft. Using the equation of motion, s = ut + (1/2)at^2, where s is the distance, u is the initial velocity (which is 0 in this case), t is the time, and a is the acceleration due to gravity, we can calculate the distance. Since the stone is falling, the acceleration due to gravity is -9.8 m/s^2. Plugging in the values, we get s = 0 + (1/2)(-9.8)(6^2) = 0 + (-4.9)(36) = -176.4 m. However, distance cannot be negative, so we take the magnitude of -176.4 m, which is about 176.4 m. Therefore, the depth of the shaft is about 180 m.
16.
In each second of fall, the distance a freely falling object will fall is
Correct Answer
D. Increasing
Explanation
The correct answer is "increasing" because as an object falls freely, its distance of fall increases with each passing second. This is due to the acceleration of gravity, which causes the object to gain speed and cover more distance in each subsequent second. Therefore, the distance a freely falling object will fall is not a constant value like 5 m or 10 m, but rather it increases over time.
17.
A car accelerates at 2 meters/s/s. Assuming the car starts from rest, how far will it travel in 10 s?
Correct Answer
D. 100 m
Explanation
The car accelerates at a constant rate of 2 meters per second squared. This means that its velocity increases by 2 meters per second every second. Since the car starts from rest, its initial velocity is 0 meters per second. Using the equation d = v0t + (1/2)at^2, where d is the distance traveled, v0 is the initial velocity, t is the time, and a is the acceleration, we can calculate the distance traveled. Plugging in the values, we get d = 0(10) + (1/2)(2)(10)^2 = 0 + 10(10) = 100 meters. Therefore, the car will travel 100 meters in 10 seconds.
18.
Drop a rock from a 5-m height and it accelerates at 10 m/s2 and strikes the ground 1 s later. Drop the same rock from a height of 2.5 m and its acceleration of fall is about
Correct Answer
B. The same amount
Explanation
When an object is dropped, it accelerates due to the force of gravity. The acceleration is constant and equal to 9.8 m/s² near the surface of the Earth. In this case, the rock is dropped from a height of 5 m and accelerates at 10 m/s², which is twice the acceleration due to gravity. When the same rock is dropped from a height of 2.5 m, it will still experience the same acceleration due to gravity, which is 9.8 m/s². Therefore, the acceleration of fall for the rock is the same amount in both cases.
19.
A ball tossed vertically upward rises, reaches its highest point, and then falls back to its starting point. During this time the acceleration of the ball is always
Correct Answer
D. Directed downward
Explanation
The acceleration of the ball is directed downward because it is always acting in the opposite direction of the ball's velocity. When the ball is tossed upward, its velocity is initially directed upward, but as it rises, its velocity decreases until it reaches its highest point. At this point, the velocity is momentarily zero, but the acceleration is still directed downward due to the force of gravity. As the ball falls back to its starting point, its velocity becomes negative (directed downward) and the acceleration remains directed downward as well.
20.
While a car travels around a circular track at a constant speed, its
Correct Answer
D. None of the above
Explanation
While a car travels around a circular track at a constant speed, its acceleration is not zero because acceleration is the rate of change of velocity, and even though the car's speed remains constant, its direction is constantly changing as it moves in a circular path. The velocity is also not zero because velocity is the speed of an object in a given direction, and in this case, the car is moving at a constant speed in a specific direction. Inertia is not zero either because inertia is the tendency of an object to resist changes in its motion, and the car still possesses this property even while moving in a circular track. Therefore, the correct answer is none of the above.
21.
If a car accelerates from rest at 2 meters per second per second, its speed 3 seconds later will be about
Correct Answer
D. 6 m/s
Explanation
The car is accelerating at a constant rate of 2 meters per second per second. This means that its speed is increasing by 2 meters per second every second. After 3 seconds, the car would have increased its speed by 2 meters per second three times, resulting in a speed of 6 meters per second.
22.
A ball is thrown upwards and returns to the same position. Compared with its original speed after release, its speed when it returns is about
Correct Answer
B. The same
Explanation
When the ball is thrown upwards and returns to the same position, its speed when it returns is the same as its original speed after release. This is because the gravitational force acting on the ball causes it to decelerate as it moves upwards, eventually bringing it to a stop. As the ball starts to fall back down, it accelerates due to the gravitational force, and its speed increases. However, at the same height from which it was released, its speed is the same as its original speed after release. Therefore, the correct answer is "the same."
23.
An object covers a distance of 8 meters in the first second of travel, another 8 meters during the next second, and 8 meters again during the third second. Its acceleration in meters per second per second is approximately
Correct Answer
A. 0
Explanation
The object covers the same distance of 8 meters in each second of travel, indicating that its velocity remains constant. Since acceleration is the rate of change of velocity, and the velocity does not change, the acceleration is 0.
24.
At one instant an object in free fall is moving downward at 50 meters per second. One second later its speed should be about
Correct Answer
D. 60 m/s
Explanation
When an object is in free fall, its speed increases by approximately 9.8 meters per second every second due to the acceleration due to gravity. Therefore, one second later, the object's speed should increase by 9.8 m/s, resulting in a speed of approximately 59.8 m/s. Since this is closest to 60 m/s, the correct answer is 60 m/s.
25.
At one instant a heavy object in air is moving upward at 50 meters per second. One second later its speed is approximately
Correct Answer
A. 40 m/s
Explanation
The object is moving upward at a speed of 50 m/s. However, one second later, the object would experience the force of gravity acting on it, causing its velocity to decrease. Therefore, its speed would be less than 50 m/s. The closest option is 40 m/s, which would be the approximate speed of the object one second later.
26.
Disregarding air resistance, objects fall with constant
Correct Answer
C. Acceleration
Explanation
Objects fall with constant acceleration. This means that the speed at which an object falls increases at a constant rate with each passing second. This is due to the force of gravity acting on the object, causing it to accelerate towards the ground. The acceleration due to gravity on Earth is approximately 9.8 meters per second squared. Therefore, objects do not fall with constant velocity or speed, as these would imply no change in motion. Additionally, objects do not fall with constant distances each successive second, as their displacement increases with time due to the acceleration.
27.
A ball is thrown upwards and caught when it comes back down. In the presence of air resistance, the speed with which it is caught is always
Correct Answer
B. Less than the speed it had when thrown upwards
Explanation
When a ball is thrown upwards and caught when it comes back down, the presence of air resistance causes it to lose some of its initial kinetic energy. As a result, the speed with which it is caught is always less than the speed it had when thrown upwards. This is because air resistance acts as a force opposing the motion of the ball, causing it to slow down as it moves upward and then accelerate downward due to the force of gravity. Therefore, the ball loses some of its initial speed and is caught at a lower speed than it was thrown upwards.
28.
Starting from rest, the distance a freely falling object will fall in 0.5 second is about
Correct Answer
D. None of the above
Explanation
The distance a freely falling object will fall in 0.5 seconds is not 1 meter or 10 meters. The correct answer is "none of the above" because the distance an object falls in a given time depends on the acceleration due to gravity, which is approximately 9.8 meters per second squared. Using the equation d = 0.5 * g * t^2, where d is the distance, g is the acceleration due to gravity, and t is the time, we can calculate that the distance fallen in 0.5 seconds is approximately 1.225 meters. Therefore, none of the given options accurately represent the distance fallen in 0.5 seconds.
29.
One half second after starting from rest, a freely falling object will have a speed of about
Correct Answer
C. 5 m/s
Explanation
When an object is freely falling, it accelerates due to gravity at a rate of 9.8 m/s². After half a second, the object would have been accelerating for 0.5 seconds. Using the equation v = u + at, where v is the final velocity, u is the initial velocity (which is 0 in this case), a is the acceleration, and t is the time, we can calculate the final velocity. Plugging in the values, we get v = 0 + (9.8 * 0.5) = 4.9 m/s. Therefore, the speed of the object after half a second would be approximately 5 m/s.
30.
An object falls freely from rest on a planet where the acceleration due to gravity is 20 meters per second squared. After 5 seconds, the object will have a speed of
Correct Answer
E. 100 m/s
Explanation
The object falls freely under the influence of gravity, so its velocity will increase at a constant rate. The acceleration due to gravity on this planet is 20 m/s^2, which means that every second, the object's velocity will increase by 20 m/s. After 5 seconds, the object's velocity will be 20 m/s * 5 s = 100 m/s.
31.
An object falls freely from rest on a planet where the acceleration due to gravity is twice as much as it is on Earth. In the first 5 seconds it falls a distance of
Correct Answer
C. 250 m
Explanation
On Earth, the acceleration due to gravity is approximately 9.8 m/s². Since the acceleration due to gravity on the given planet is twice as much, it would be 2 * 9.8 m/s² = 19.6 m/s². Using the equation for the distance fallen by an object in free fall, d = 0.5 * g * t², where d is the distance, g is the acceleration due to gravity, and t is the time, we can calculate the distance fallen in the first 5 seconds. Plugging in the values, we get d = 0.5 * 19.6 m/s² * (5 s)² = 0.5 * 19.6 m/s² * 25 s² = 245 m. Therefore, the correct answer is 250 m.
32.
An apple falls from a tree and hits the ground 5 meters below. It hits the ground with a speed of about
Correct Answer
B. 10 m/s
Explanation
The apple falls from a tree, which means it is subject to the force of gravity pulling it downwards. As it falls, it accelerates due to this force. The speed at which it hits the ground can be estimated using the equation v = sqrt(2gh), where v is the final velocity, g is the acceleration due to gravity (approximately 9.8 m/s^2), and h is the height from which the apple fell (5 meters in this case). Plugging in the values, we get v = sqrt(2 * 9.8 * 5) ≈ 10 m/s. Therefore, the correct answer is 10 m/s.
33.
It takes 6 seconds for a stone to fall to the bottom of a mine shaft. How deep is the shaft?
Correct Answer
C. About 180 m
Explanation
The time it takes for an object to fall is determined by the height from which it falls and the acceleration due to gravity. In this case, since it takes 6 seconds for the stone to fall, we can use the equation h = (1/2)gt^2, where h is the height, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time. Plugging in the values, we get h = (1/2)(9.8)(6)^2 = 176.4 m. Therefore, the depth of the shaft is approximately 180 m.
34.
If you drop an object, it will accelerate downward at a rate of 9.8 meters per second per second. If you instead throw it downwards, its acceleration (in the absence of air resistance) will be
Correct Answer
B. 9.8 meters per second per second
Explanation
When an object is dropped, it falls freely under the influence of gravity. The acceleration due to gravity is constant and equal to 9.8 meters per second per second. When an object is thrown downward, it still experiences the same acceleration due to gravity. Therefore, the object's acceleration, in the absence of air resistance, will also be 9.8 meters per second per second.
35.
In each second of fall, the distance a freely falling object will fall is
Correct Answer
D. Increasing
Explanation
The correct answer is "increasing". This means that the distance a freely falling object will fall in each second of fall is increasing. This is because the object accelerates due to the force of gravity. As time passes, the object's speed and therefore the distance it falls in each second increases.
36.
If a projectile is fired straight up at a speed of 10 m/s, the time it takes to reach the top of its path is about
Correct Answer
A. 1 second
Explanation
When a projectile is fired straight up, its initial velocity is in the opposite direction of gravity. As the projectile moves upward, gravity acts as a decelerating force, eventually bringing it to a stop at the top of its path. At this point, the projectile starts to fall back down. The time it takes to reach the top of its path can be estimated by considering the initial velocity and the acceleration due to gravity. Since the initial velocity is 10 m/s and the acceleration due to gravity is approximately 9.8 m/s^2, it takes approximately 1 second for the projectile to reach the top of its path.
37.
If a projectile is fired straight up at a speed of 10 m/s, the total time to return to its starting position is about
Correct Answer
B. 2 seconds
Explanation
The time it takes for a projectile to return to its starting position can be estimated by considering the motion of the object. When a projectile is fired straight up, it will reach its highest point (the peak of its trajectory) and then fall back down. The time it takes for the projectile to reach its highest point is half of the total time it takes to return to its starting position. Therefore, if the total time is estimated to be 2 seconds, it means that the projectile takes 1 second to reach its highest point and another 1 second to fall back down, resulting in a total time of 2 seconds.
38.
Consider drops of water that leak at a steady rate from a dripping faucet. As the drops fall they
Correct Answer
B. Get farther apart
Explanation
As the drops of water fall from a dripping faucet, they experience air resistance and gravity. Over time, the air resistance causes the drops to slow down, and gravity pulls them downward. This combination of forces causes the drops to gradually increase the distance between each other as they fall, resulting in them getting farther apart.
39.
Disregarding air drag, how fast must you toss a ball straight up in order for it to take 2 seconds to return to the level from which you tossed it?
Correct Answer
C. 10 m/s
Explanation
To calculate the speed at which the ball must be tossed, we can use the equation of motion for vertical motion. The time taken for the ball to reach its highest point and return to the same level is the total time of 2 seconds. Since the ball is thrown straight up, the initial velocity is positive and the final velocity when it returns is negative. Using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration (which is -9.8 m/s^2 for objects moving upwards), and t is the time, we can substitute the given values. Rearranging the equation, we get u = v - at. Substituting v = -u, t = 2 seconds, and a = -9.8 m/s^2, we can solve for u. u = -(-u) - (-9.8 m/s^2)(2 s). Simplifying the equation, we get 2u = 19.6 m/s^2. Solving for u, we find u = 9.8 m/s. Therefore, the ball must be tossed with a speed of 10 m/s upwards to take 2 seconds to return to the starting level.
40.
A car accelerates at 2 meters per second per second. Assuming the car starts from rest, how much time does it need to accelerate to a speed of 30 m/s?
Correct Answer
B. 15 seconds
Explanation
The car is accelerating at a rate of 2 meters per second per second. This means that its speed is increasing by 2 meters per second every second. If the car starts from rest, it needs to reach a speed of 30 m/s. Since the rate of acceleration is constant, we can use the equation v = u + at, where v is the final velocity, u is the initial velocity (which is 0 in this case), a is the acceleration, and t is the time. Plugging in the values, we get 30 = 0 + 2t. Solving for t, we find that t = 15 seconds. Therefore, it takes 15 seconds for the car to accelerate to a speed of 30 m/s.
41.
A car accelerates from rest for 5 seconds until it reaches a speed of 20 m/s. What is the car's acceleration in meters per second per second?
Correct Answer
D. 4
Explanation
The car's acceleration can be calculated using the formula: acceleration = (final velocity - initial velocity) / time. In this case, the final velocity is 20 m/s, the initial velocity is 0 m/s (since the car starts from rest), and the time is 5 seconds. Plugging these values into the formula, we get: acceleration = (20 m/s - 0 m/s) / 5 s = 4 m/s^2. Therefore, the car's acceleration is 4 meters per second per second.
42.
Ten seconds after starting from rest, a car is moving at 40 m/s. What is the car's acceleration in meters per second per second?
Correct Answer
C. 4.0
Explanation
The car's acceleration can be calculated using the formula: acceleration = (final velocity - initial velocity) / time. In this case, the final velocity is 40 m/s, the initial velocity is 0 m/s (since the car started from rest), and the time is 10 seconds. Plugging these values into the formula, we get acceleration = (40 m/s - 0 m/s) / 10 s = 4 m/s^2. Therefore, the car's acceleration is 4.0 meters per second per second.
43.
When a rock thrown straight upwards gets to the exact top of its path, its
Correct Answer
B. Velocity is zero and its acceleration is about 10 meters per second per second
Explanation
When a rock thrown straight upwards gets to the exact top of its path, its velocity is zero because it momentarily stops moving before it starts falling back down. Its acceleration is about 10 meters per second per second because it experiences a constant acceleration due to gravity pulling it downwards. This means that its speed decreases at a rate of 10 meters per second every second until it reaches the top of its path.
44.
A bullet is dropped from the top of the Empire State Building while another bullet is fired downward from the same location. Neglecting air resistance, the acceleration of
Correct Answer
C. Each bullet is 9.8 meters per second per second
Explanation
Each bullet experiences the same acceleration of 9.8 meters per second per second due to gravity, regardless of whether it is dropped or fired downward. This is because the acceleration due to gravity is a constant value on Earth. The initial velocity of the bullets does not affect their acceleration. Therefore, both bullets experience the same acceleration of 9.8 meters per second per second.
45.
The muzzle velocity of a bullet fired from a new rifle is 100 m/s. Neglecting air resistance, at the end of one second a bullet fired straight up into the air will have traveled a distance of
Correct Answer
A. (100 - 4.9) m
Explanation
The correct answer is (100 - 4.9) m. This is because the bullet is fired straight up into the air, meaning it is subject to the force of gravity pulling it downwards. The bullet will experience a constant acceleration of 9.8 m/s^2 due to gravity. Using the equation of motion, s = ut + (1/2)at^2, where s is the distance traveled, u is the initial velocity, t is the time, and a is the acceleration, we can calculate the distance traveled at the end of one second. Plugging in the values, s = 100(1) + (1/2)(-9.8)(1)^2 = 100 - 4.9 = 95.1 m.
46.
A bullet is fired straight down from the top of a high cliff. Neglecting air resistance, the acceleration of the bullet in meters per second per second
Correct Answer
B. Is 9.8
Explanation
The acceleration of the bullet is 9.8 meters per second per second because when an object is in free fall near the surface of the Earth, it experiences a constant acceleration due to gravity of approximately 9.8 m/s^2. This means that the bullet's velocity will increase by 9.8 meters per second every second it falls.
47.
A bullet is dropped into a river from a very high bridge. At the same time, another bullet is fired from a gun, straight down towards the water. Neglecting air resistance, the acceleration just before striking the water
Correct Answer
C. Is the same for each bullet
Explanation
The acceleration just before striking the water is the same for each bullet. This is because both bullets are subject to the same gravitational acceleration, regardless of how they were initially propelled. Neglecting air resistance, all objects near the surface of the Earth experience the same acceleration due to gravity, which is approximately 9.8 m/s². Therefore, both the dropped bullet and the fired bullet will have the same acceleration just before striking the water.
48.
Someone standing at the edge of a cliff throws one ball straight up and another ball straight down at the same initial speed. Neglecting air resistance, the ball to hit the ground below the cliff with the greater speed will be
Correct Answer
C. Neither -- they will both hit with the same speed
Explanation
Both balls will hit the ground with the same speed because the initial speed at which they were thrown is the same. The only difference is the direction in which they were thrown, but gravity affects both balls equally and accelerates them at the same rate. Therefore, they will both hit the ground with the same speed.
49.
A ball is thrown upwards. Neglecting air resistance, what initial upward speed does the ball need to remain in the air for a total time of 10 seconds?
Correct Answer
A. About 50 m/s
Explanation
To remain in the air for a total time of 10 seconds, the ball needs to reach its maximum height and then fall back down within that time frame. The time it takes for the ball to reach its maximum height is half of the total time, so 10/2 = 5 seconds. Using the equation v = u + at, where v is the final velocity, u is the initial velocity, a is the acceleration (which is equal to -9.8 m/s^2 due to gravity), and t is the time, we can solve for the initial upward speed. Plugging in the values, we get 0 = u - 9.8 * 5. Solving for u, we find that the initial upward speed should be approximately 49 m/s, which is closest to 50 m/s.
50.
A ball is thrown 125 meters upward and then falls the same distance back to Earth. Neglecting air resistance, its total time in the air is
Correct Answer
B. About 10 seconds
Explanation
When a ball is thrown upward and then falls back to Earth, it follows a parabolic trajectory. The time it takes for the ball to reach its maximum height is equal to the time it takes for it to fall back down to the ground. This means that the time spent going up is equal to the time spent going down. Since the total distance traveled by the ball is 125 meters, and it spends an equal amount of time going up and coming down, the total time in the air would be approximately 10 seconds.