Final answer:
To determine the average force exerted by the floor on the ball, we calculate the change in momentum and divide by the collision time. We find the change in momentum by subtracting the initial momentum from the final momentum and then apply the impulse-momentum theorem to compute the average force.
Step-by-step explanation:
To solve the problem involving the basketball player dropping the ball, we can use the impulse-momentum theorem, which states that the impulse exerted on an object is equal to the change in the object's momentum. First, we calculate the momentum of the basketball just before and just after it strikes the floor, and then we calculate the impulse to find the average force exerted by the floor during the collision.
The initial momentum (pi) of the ball just before hitting the floor is the mass of the ball (m) multiplied by its velocity (vi), so pi = m × vi. After the collision, the final momentum (pf) is m × vf, where vf is the rebound velocity. The change in momentum (Δp) is given by pf - pi.
Knowing that impulse (J) is the change in momentum, we can write J = Δp = m × vf - m × vi. The average force (F) exerted by the floor can be found by dividing the impulse by the time interval (Δt) of the collision: F = J / Δt. Substituting the values, we get F = (m × vf - m × vi) / Δt.
Let's plug in the values: m = 0.60 kg, vi = 6.3 m/s (downward, so we take this as negative), vf = 5.3 m/s (upward, so this is positive), and Δt = 0.12 s. Calculate the change in momentum Δp = (0.60 kg × 5.3 m/s) - (0.60 kg × -6.3 m/s). Then, calculate the average force F = Δp / 0.12 s. Finally, state the magnitude and direction of the average force.