Kinematics 4 Question 8
8. 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
(2000, 2M) (a)
(c)
(b)
(d)
Objective Question II (One or more correct option)
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Solution:
- (i) For uniformly accelerated/decelerated motion
$$ v^{2}=u^{2} \pm 2 g h $$
i.e. $v-h$ graph will be a parabola (because equation is quadratic). (ii) Initially velocity is downwards ( $-ve)$ and then after collision, it reverses its direction with lesser magnitude, i.e. velocity is upwards (+ve). Graph (a) satisfies both these conditions.
NOTE At time $t=0$ corresponds to the point on the graph where $h=d$.
