A ball is dropped vertically from a height d above the ground. It hits the ground and bounces up vertically to a height d/2 , Neglecting subsequent motion and air resistance, its velocity v varies with height h above the ground as

Question

A ball is dropped vertically from a height d above the ground. It hits the ground and bounces up vertically to a height d/2 , Neglecting subsequent motion and air resistance, its velocity v varies with height h above the ground as (A) Option 1

(B)

(C)

(D)

Tardigrade Admin · Accepted Answer

(i) For uniformly accelerated/deaccelerated motion,

v^{2} = u^{2} \pm 2 g h

i.e., v - h graph will be a parabola (because the equation is quadratic).
(ii) Initially, velocity is downwards (-ve) and then after the collision it reverses its direction with lesser magnitude. i.e., velocity is upwards (+ve). Graph (a) satisfies both these conditions.
Note that time

t = 0

corresponds to the point on the graph where

h = d

.

Q. A ball is dropped vertically from a height d above the ground. It hits the ground and bounces up vertically to a height d/2 , Neglecting subsequent motion and air resistance, its velocity v varies with height h above the ground as

Q. A ball is dropped vertically from a height $d$ above the ground. It hits the ground and bounces up vertically to a height $d /2$ , Neglecting subsequent motion and air resistance, its velocity $v$ varies with height $h$ above the ground as