Answer :
Final answer:
The basketball player experiences an impulse of 97.515 kg·m/s in the downward direction. The force exerted by the floor before the jump is 578.58 N. The total average force exerted by the floor during the jump is 216.7 N.
Explanation:
To calculate the impulse experienced by the basketball player, we need to use the formula:
Impulse = Change in Momentum
The momentum of an object is given by the product of its mass and velocity:
Momentum = mass × velocity
Given that the mass of the basketball player is 59.1 kg and the velocity with which they leave the floor is 1.65 m/s upward, we can calculate the initial momentum:
Initial Momentum = 59.1 kg × 1.65 m/s = 97.515 kg·m/s
Since the player is moving upward, the final momentum is zero as they come to a stop at the highest point of their jump. Therefore, the change in momentum is:
Change in Momentum = Final Momentum - Initial Momentum = 0 - 97.515 kg·m/s = -97.515 kg·m/s
The magnitude of the impulse experienced by the player is the absolute value of the change in momentum:
Magnitude of Impulse = |-97.515 kg·m/s| = 97.515 kg·m/s
The direction of the impulse is downward, as the player is moving upward.
To calculate the force exerted by the floor before the jump, we can use Newton's second law of motion:
Force = Mass × Acceleration
Since the player is initially at rest on the floor, their initial velocity is zero. The acceleration due to gravity is approximately 9.8 m/s². Therefore, the force exerted by the floor is:
Force = 59.1 kg × 9.8 m/s² = 578.58 N
The magnitude of the force exerted by the floor is 578.58 N.
To calculate the total average force exerted by the floor during the jump, we can use the formula:
Average Force = Impulse / Time
Given that the player is in contact with the floor for 0.450 s, we can calculate the average force:
Average Force = 97.515 kg·m/s / 0.450 s = 216.7 N
The magnitude of the total average force exerted by the floor is 216.7 N.
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