To make a bounce pass, a player throws a 0.60-kg basketball toward the floor. The ball hits the floor with a speed of 5.2 m/s at an angle of 60 ∘ to the vertical.

Part A
If the ball rebounds with the same speed and angle, what was the magnitude of the impulse delivered to it by the floor?

impulse = change of momentum

all vertical, no change in horizontal
speed from -v cos 60 to + v cos 60

2 m v cos 60

To find the magnitude of the impulse delivered to the ball by the floor, we can use the principle of conservation of momentum.

Impulse can be calculated using the equation:

Impulse = change in momentum

Since the ball rebounds with the same speed and angle, the change in momentum is zero. Therefore, the impulse delivered to the ball by the floor is also zero.

Hence, the magnitude of the impulse delivered to the ball by the floor is zero.

To answer this question, we need to understand the concept of impulse. Impulse is defined as the change in momentum of an object, and it is equal to the force applied to an object multiplied by the time interval over which the force is applied.

In this scenario, the impulse delivered to the ball by the floor can be calculated by using the principle of conservation of momentum. The initial momentum of the ball, before it hits the floor, is equal to its mass multiplied by its initial velocity. The final momentum of the ball, after it rebounds off the floor, is equal to its mass multiplied by its final velocity.

To find the final velocity of the ball after the bounce, we can break down the initial velocity into its vertical and horizontal components. The vertical component remains the same, as there is no acceleration in that direction. However, the horizontal component is reversed after the bounce due to the change in direction.

Using trigonometry, we can find the vertical component of the velocity after the bounce:
v_y = v_initial × sin(angle)

Similarly, we can find the horizontal component of the velocity after the bounce:
v_x = -v_initial × cos(angle)

Since the magnitude of the impulse is equal to the change in momentum, we can calculate it using the equation:
Impulse = m × (vf - vi)

Since the ball has the same magnitude of velocity after the bounce (rebound), the final velocity (vf) is the negative of the initial velocity (vi). Therefore, the impulse can be simplified as:
Impulse = m × (vf - vi) = -2mvi

Given the mass of the basketball (m = 0.60 kg) and the initial velocity (vi = 5.2 m/s), we can calculate the magnitude of the impulse delivered to the ball by the floor as follows:

Impulse = -2 × 0.60 kg × 5.2 m/s

Calculating this expression will give us the result for Part A.