A small rubber ball can be made to rebound to suprising heights by holding it on

Question

A small rubber ball can be made to rebound to suprising heights by holding it on top of a heavier ball, then dropping the two together as shown below. Model the result of dropping a 50.0-g rubber ball and a 600.-g basketball together. Take the original height of the bottom of the basketball to be h=1.50 m from the floor and the coefficient of restitution to be 0.800 for all collisions. First disregard the smaller ball and consider only the collision of the basketball with the floor. Then let the downward moving rubber ball collide with the upward moving basketball, which has a diameter of 24.0 cm. How high does the small rubber ball rise?

Explanation / Answer

Velocity of basket ball just before it hits the ground: Vf^2 = Vi^2 + 2ad Vf = sqrt(2*9.8*1.5) Vf = 5.42m/s Velocity after rebound: V_rebound = COR * Vf V_rebound = .8*5.48 = 4.33m/s ------------------------------------------ Velociyt of rubber ball right before impact: Same as basketball they both fall the same distance; 5.42m/s Impact velocity: The rubber ball will collide with the basketball with a speed equal to the velocity of the basekt ball on its rebound plus the velocity of the falling rubber ball Velocity of impact = 5.42 + 4.33 = 9.75m/s V_rubberball_rebound = .8 * 9.75 = 7.8ms/

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