Answer to Question #130352 in Physics for Elvis

Question

1.A ball of mass1kg is dropped from a height of 7m and rebounds to a height of 4.5m. Calculate: (a) its Kinetic Energy just before impact. (b) its initial rebound velocity and Kinetic Energy. Account for the loss of Kinetic Energy on impact.

Answer 1

(a) kinetic energy of a ball just before impact

$$KE_1=\frac{mv^2}{2}=mgh_1\\ =1\:\rm kg\times 9.8\: N/kg\times 7\: m=68.6\: J$$

(b) the initial rebound kinetic energy of a ball

$$KE_2=\frac{mv_2^2}{2}=mgh_2\\ =1\:\rm kg\times 9.8\: N/kg\times 4.5\: m=44.1\: J$$

the initial rebound velocity of a ball

$$v_2=\sqrt{2gh_2}=\sqrt{2\times 9.8\:\rm N/kg\times 4.5\: m}=9.4\:\rm m/s$$