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 5.5 m/s at an angle of 59° from the vertical. If the ball rebounds with the same speed and angle, what was the impulse delivered to it by the floor?

Question

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 5.5 m/s at an angle of 59° from the vertical. If the ball rebounds with the same speed and angle, what was the impulse delivered to it by the floor?

Answer 1

The impulse delivered by the floor equals the momentum change in the vertical direction.

That is equal to 2*M*Vcos55

The horizontal velocity component does not change during the bounce.

Answer 2

In this case, I=2MVsin31

Answer 3

To find the impulse delivered to the basketball by the floor, we need to apply the impulse-momentum principle. The principle states that the change in momentum of an object is equal to the impulse applied to it. In equation form, it is written as:

Impulse = Change in momentum

The impulse is the force applied to the object multiplied by the time it is applied. In this case, since the basketball hits the floor and rebounds with the same speed and angle, we can assume that the contact time is very short and can be neglected. Therefore, we can simplify the equation to:

Impulse = Change in momentum = Final momentum - Initial momentum

Now let's find the initial momentum and final momentum of the basketball.

Initial momentum:
The initial momentum of the basketball can be obtained from its velocity before bouncing. We know the magnitude of the velocity (5.5 m/s) and the angle (59°), so we can calculate its vertical and horizontal components.

Initial vertical momentum (before bouncing):
Vertical momentum = Initial velocity * mass *cos(angle)
= 5.5 m/s * 0.60 kg * cos(59°)

Initial horizontal momentum (before bouncing):
Horizontal momentum = Initial velocity * mass * sin(angle)
= 5.5 m/s * 0.60 kg * sin(59°)

Final momentum:
The final momentum of the basketball after bouncing will have the same magnitude (5.5 m/s) but with an opposite sign. We assume that no external forces act on the basketball in the horizontal direction, so the horizontal momentum remains the same. Therefore, only the vertical momentum changes sign.

Final vertical momentum (after bouncing):
Vertical momentum = -Initial vertical momentum

Now we can calculate the impulse.

Impulse = Change in momentum = Final momentum - Initial momentum

Impulse = (-Initial vertical momentum) - Initial horizontal momentum

Plug in the values and calculate to find the answer.