Question

You throw a ball straight up, and it lands with 2/3 the speed with which you threw it. What fraction of the initial kinetic energy was lost during the time the ball was in the air?

Answer 1

let vi is the initial speed.

so, final speed, vf = (2/3)*vi

let m is the mass of the ball.

KEi = (1/2)*m*vi^2

KEf = (1/2)*m*vf^2

= (1/2)*m*((2/3)*vi)^2

= (4/9)*(1/2)*m*vi^2

The fraction of the initial kinetic energy was lost during the time the ball was in the air = (KEi - KEf)/KEi

= ((1/2)*m*vi^2 - (4/9)*(1/2)*m*vi^2 )/((1/2)*m*vi^2 )

= 1 - 4/9

= 5/9 (or) 0.556 <<<<<<<<-------------Answer