Explanation The two balls are initially at rest and undergo free fall until they reach earth. According to conservation of energy, the potential energy at the initial height must be equal to kinetic energy at final point. Write the expression for the conservation of energy of ball falling from a height h . m g h = 1 2 m v 2 (I) Here, m is the mass of ball, g is the acceleration due to gravity, h is the initial height of ball and v is the speed of the ball before colliding with ground. Rearrange above equation to get v . v = 2 g h Above equation implies that, velocity of free fall is independent of mass but depends only on initial height. Take upward as + y direction. Both basketball and tennis ball are dropped from same height. Thus, from above equation, both of them have same speed before colliding with the ground. Write the expression for the velocity of basketball just before it collides with the ground. v → b = − 2 g h j ^ (II) Here, v → b is the velocity of basketball just before it collides with the ground and j ^ is the unit vector along + y direction. Write the expression for the velocity of tennis ball just before the basketball collides with the ground. v → t , i = − 2 g h j ^ (III) Here, v → t , i is the velocity of tennis ball the instant before the basketball collides with the ground. The collision of basketball with earth can be considered as elastic collision of an object with massive object at rest. This case is similar to impact of projectile with massive Earth and in such a case, the projectile will leave the ground with velocity equal in magnitude and opposite in direction as that of incident velocity. Write the expression for the final velocity of basketball. v → b , i = − v → b Here, v → b , i is the velocity of basketball after collision with ground. Put equation (II) in the above equation. v → b , i = 2 g h j ^ (IV) Consider the elastic collision of basketball and tennis ball. Assume that before this collision tennis ball is travelling downward at speed given in equation (III) and the basketball is travelling upwards with velocity obtained in equation (IV). Equation (IV) also represents the velocity of the basketball just before the collision with the tennis ball and the velocity of the tennis ball before its collision with the basketball is given by equation (III). Write the expression for the velocity of tennis ball after the collision with the basketball. v → t , f = m t − m b m t + m b v → t , i + 2 m b m t + m b v → b , i Here, v → t , f is the velocity of tennis ball the instant after it collides with basketball, m t is the mass of tennis ball and m b is the mass of basketball. Put equations (III) and (IV) in the above equation. v → t , f = m t − m b m t + m b ( − 2 g h j ^ ) + 2 m b m t + m b ( 2 g h j ^ ) = 3 m b − m t m t + m b ( 2 g h j ^ ) (V) Equation (I) can be applied also for the tennis ball as it reaches the initial position after the collision to the maximum height

Physics for Scientists and Engineers: Foundations and Connections

1st Edition

ISBN: 9781133939146

Author: Katz, Debora M.

Publisher: Cengage Learning

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Chapter 11, Problem 77PQ

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Chapter 11, Problem 76PQ

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Chapter 11 Solutions

Physics for Scientists and Engineers: Foundations and Connections

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The maximum height reached by the tennis ball after the balls collide with the ground.

Solution Summary: The author explains that the maximum height reached by the tennis ball after the balls collide with the ground is 9.8m.

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