1.
A stone with an initial velocity of zero is dropped from a bridge above a river. After 3 s, the stone strikes the water below the bridge. Approximately how fast is the stone traveling when it strikes the water?
Correct Answer
C. 30 m/s
Explanation
When the stone is dropped from the bridge, its initial velocity is zero. As it falls, it accelerates due to the force of gravity. The acceleration due to gravity is approximately 9.8 m/s^2. After 3 seconds, the stone would have been accelerating for 3 seconds, reaching a velocity of 9.8 m/s^2 * 3 s = 29.4 m/s. Since the stone is traveling downwards, the speed is positive, so the stone is traveling approximately 30 m/s when it strikes the water.
2.
A ball is projected vertically upwards with an initial velocity of 50 m/s. Using the formula 'v = u + at,' what is the calculated velocity after 2s?
Correct Answer
B. 30.4 m/s
Explanation
The formula v = u + at is used to calculate the final velocity of an object when it is projected vertically upwards. In this case, the initial velocity (u) is given as 50 m/s and the time (t) is given as 2 seconds. Since the ball is projected upwards, the acceleration (a) due to gravity is -9.8 m/s^2. Plugging these values into the formula, we get v = 50 + (-9.8)(2) = 50 - 19.6 = 30.4 m/s. Therefore, the calculated velocity after 2 seconds is 30.4 m/s.
3.
The diagram below shows a football being kicked. Angle θ represents the angle between the horizontal and the ball's initial direction of motion. Which value of θ would result in the ball traveling the longest distance?
Correct Answer
B. 45 degrees
Explanation
A 45-degree angle would result in the ball traveling the longest distance. This is because at this angle, the ball is launched with a combination of vertical and horizontal velocities that maximize the range. At angles smaller than 45 degrees, the vertical velocity component increases, causing the ball to spend more time in the air and reducing the horizontal distance traveled. At angles larger than 45 degrees, the horizontal velocity component decreases, resulting in a shorter range. Therefore, a 45-degree angle provides the optimal balance between vertical and horizontal velocities for maximum distance.
4.
If a golf ball is hit with more force at the same angle, its initial acceleration will
Correct Answer
B. Increase
Explanation
When a golf ball is hit with more force at the same angle, its initial acceleration will increase. This is because force and acceleration are directly proportional according to Newton's second law of motion. When the force applied to an object increases, its acceleration also increases. Therefore, hitting the golf ball with more force will result in a higher initial acceleration.
5.
A pitching machine launches a softball horizontally with no spin. Which of the following statements correctly describes the ball’s motion in the air if the machine is set so that the launch speed is increased?
Correct Answer
D. The ballâ€™s velocity increases and the distance the ball falls in one-second remains the same
Explanation
As the launch speed of the pitching machine increases, the ball's velocity also increases. This is because the launch speed directly affects the initial velocity of the ball. However, the distance the ball falls in one-second remains the same. This is because the ball is launched horizontally with no spin, so it experiences only the force of gravity pulling it downwards. The force of gravity acts vertically and does not affect the horizontal motion of the ball. Therefore, the distance the ball falls in one-second remains constant regardless of the increase in velocity.
6.
A punter on the football team can kick the ball at an angle of either 30° or 80°. If he wants to maximize the distance the ball travels, at which angle should he kick the ball?
Correct Answer
A. The 30Â° angle because the ball goes further
Explanation
The correct answer is the 30Â° angle because the ball goes further. When a ball is kicked at an angle, its horizontal and vertical components of velocity determine its trajectory. At a 30Â° angle, the ball has a larger horizontal velocity component compared to an 80Â° angle. This means that the ball will cover more horizontal distance before hitting the ground, resulting in a greater overall distance traveled. The vertical component of velocity does not affect the distance traveled, so the time spent in the air is not a determining factor in this case.
7.
A soccer ball is kicked so that at the peak of its trajectory, it has a horizontal speed of 21 m/s, and is 6 meters above the ground. The entire flight takes 2.2 seconds. How far away from the kicker does the soccer ball land?
Correct Answer
D. 46.2 meters
Explanation
The soccer ball is kicked with a horizontal speed of 21 m/s and reaches its peak at a height of 6 meters above the ground. Since there is no vertical acceleration, the time taken to reach the peak is half of the total flight time, which is 2.2 seconds. Therefore, the time taken to reach the peak is 1.1 seconds. Using the equation of motion, we can calculate the horizontal distance traveled by the ball using the formula distance = speed Ã— time. Thus, the horizontal distance traveled by the ball is 21 m/s Ã— 2.2 seconds = 46.2 meters.
8.
A diver jumps horizontally off a cliff with an initial velocity of 6.0 m/s. The diver strikes the water 3.5 s later.
a) What is the approximate vertical speed of the diver upon reaching the surface of the water?
b) What is the horizontal speed of the diver 2.5 seconds after the diver jumps?
c) How far from the base of the cliff will the diver strike the water?
9.
Two objects are released from the same height. Object A falls straight down from the cliff, and object B follows a curved parabolic path. Which of these is true?
Correct Answer
D. A and B hit the ground at the same time.
Explanation
The statement "A and B hit the ground at the same time" is true because both objects are released from the same height. In the absence of any external forces, such as air resistance, objects will fall towards the ground with the same acceleration due to gravity. Therefore, both objects will take the same amount of time to reach the ground, regardless of their paths or weights.
10.
Projectile motion has two components, horizontal (x) and vertical (y) as can be seen below. The horizontal motion has:
Correct Answer
C. Constant velocity
Explanation
In projectile motion, the horizontal component of motion remains constant. This is because there is no force acting horizontally on the object, so there is no acceleration in the horizontal direction. As a result, the velocity in the horizontal direction remains constant throughout the motion.
11.
A cannon fires a 1kg cannonball with a velocity of 100m/s at 60 degrees to the horizontal and from a cliff which is 20m above sea level. What is the vertical component of its velocity?
Correct Answer
B. 86.6m/s
Explanation
When a projectile is launched at an angle to the horizontal, its velocity can be broken down into two components: the horizontal component and the vertical component. The vertical component of velocity determines the projectile's motion in the vertical direction. In this case, the cannonball is launched at a 60-degree angle to the horizontal, which means that the vertical component of velocity can be calculated using trigonometry. The vertical component of velocity can be found by multiplying the initial velocity (100 m/s) by the sine of the launch angle (60 degrees). Applying this formula, we get: vertical velocity = 100 m/s * sin(60 degrees) = 100 m/s * 0.866 = 86.6 m/s. Therefore, the correct answer is 86.6 m/s.
12.
A cannon fires a 1kg cannonball with a velocity of 100m/s at 60 degrees to the horizontal and from a cliff which is 20m above sea level
How high will it reach?
Correct Answer
A. 127m
Explanation
When the cannonball is fired at an angle of 60 degrees to the horizontal, it will have two components of velocity: one in the horizontal direction and one in the vertical direction. The horizontal component of velocity remains constant throughout the motion, while the vertical component changes due to the force of gravity. At the highest point of its trajectory, the vertical component of velocity becomes zero, and the cannonball starts to fall back down. The time taken to reach the highest point can be calculated using the vertical component of velocity and the acceleration due to gravity. Using this time, the maximum height can be calculated using the equation for vertical displacement. In this case, the maximum height is 127m.
13.
When a ball is projected horizontally, what is its initial vertical velocity?
Correct Answer
A. 0
Explanation
When a ball is projected horizontally, its initial vertical velocity is 0. This is because the ball is only moving horizontally and not vertically. The initial velocity in the vertical direction is determined by the force applied in that direction, and since the ball is projected horizontally, there is no force acting vertically. Therefore, the initial vertical velocity is 0.
14.
What force acts in the y direction that causes an object to travel in a parabolic arc?
Correct Answer
C. Gravity
Explanation
Gravity is the force that acts in the y direction and causes an object to travel in a parabolic arc. This is because gravity pulls objects downwards towards the center of the Earth, causing them to follow a curved path. As the object is launched upwards, gravity slows down its vertical velocity until it reaches its maximum height, then it accelerates it downwards, resulting in a parabolic trajectory. Tension and friction do not act in the y direction, and no force would result in a straight line motion, not a parabolic arc.
15.
A man wants to shoot an arrow so that it has the greatest range (horizontal distance). At what angle should he shoot the arrow?
Correct Answer
A. 45 degrees
Explanation
The man should shoot the arrow at a 45-degree angle in order to achieve the greatest range. This is because when an object is launched at an angle of 45 degrees, it will have the maximum horizontal distance traveled due to the combination of its initial velocity and the force of gravity. At any other angle, the vertical component of the velocity would be greater, causing the object to spend more time in the air and reducing its horizontal distance.