A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy K with time t most appropriately? The figures are only illustrative and not to the scale.

Question

A tennis ball is dropped on a horizontal smooth surface. It bounces back to its original position after hitting the surface. The force on the ball during the collision is proportional to the length of compression of the ball. Which one of the following sketches describes the variation of its kinetic energy K with time t most appropriately? The figures are only illustrative and not to the scale. (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

K= (1/2) mg2t2 k propto t2 Therefore, K-t graph is parabola During collision retarding force is just like the spring force ( F propto x ) therefore kinetic energy first decreases to elastic potential energy and then increases. Most appropriate graph is therefore (b).

K=21​mg2t2 k∝t2 Therefore, K-t graph is parabola During collision retarding force is just like the spring force (F∝x) therefore kinetic energy first decreases to elastic potential energy and then increases. Most appropriate graph is therefore (b).

$K = \frac{1}{2} m g^{2} t^{2}$
$k \propto t^{2}$ Therefore, K-t graph is parabola
During collision retarding force is just like the spring force
$(F \propto x)$ therefore kinetic energy first decreases to elastic
potential energy and then increases.
Most appropriate graph is therefore (b).