Question

A basketball of mass m = 610 g rolls off the hoop's rim, falls from a height of 2.90 m to the court's floor, and then bounces up to a height of 1.50 m. (Assume up is positive. Indicate the direction with the sign of your answers.) (a) What are the magnitude and direction of the impulse delivered to the basketball by the floor? (b) If the ball is in contact with the floor for 0.165 s, what is the average force exerted on the basketball by the floor?

Answer 1

Given:

A basketball of mass m = 610 g rolls off the hoop's rim, falls from a height of 2.90 m to the court's floor, and then bounces up to a height of 1.50 m. (Assume up is positive. Indicate the direction with the sign of your answers.) (a) What are the magnitude and direction of the impulse delivered to the basketball by the floor? (b) If the ball is in contact with the floor for 0.165 s, what is the average force exerted on the basketball by the floor?

The mass of the basketball is ---   , the initial height that it drops to from the rim is --- , and the height that it bounces up to is ---    . I will call the speed with which the ball attains the instant before it hits the ground is ---    , and I will call the speed the ball attains after the collision with the ground is ---    . We can calculate from conservation of energy . The initial energy is all potential ---   and it is completely converted to kinetic energy    just befor the ball hits the ground :

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   . This is the speed before the ball hits the ground , and the velocity is :

   which means the ball is moving in the negative direction .

When the ball bounces , its initial energy is all kinetic ---   and it is comletely computed to potential energy when   --->    . We can solve for   using conservation of energy :

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===> The speed just after the collision of the basketball with the ground is :

  --- This is also the velocity of the ball just after the collision :

We then have the impulse of the ground on the basketball during the collision is :

   (1) ===>

(a)    this impulse is in the      --- SOLUTION .

(b) If we substitute   into equation (1) , we can solve for the average force :

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--- SOLUTION .