First slide

Collisions

Question

A steel ball is dropped on a hard surface from a height of 1 m and rebounds to a height of 64 cm. The maximum height attained by the ball after $n^{t h}$ bounce is (in m)

Moderate

A

${(0.64)}^{2 n}$
B

${(0.8)}^{2 n}$
C

${(0.5)}^{2 n}$
D

${(0.8)}^{n}$

Solution

$h_{n} = (e^{2 n}) h_{i}$
Given that
$f i n a l h e i g h t r i s e h_{2} = 64 c m, i n i t i a l h e i g h t o f b a l l h_{1} = 100 c m, n u m b e r o f c o l l i s i o n s n = 1$
$h_{2} = (e^{2}) h_{1}$
(64 cm) = ( $e^{2}$ )(100cm)
$∴$ e = 0.8
Substituting in Eq.(i) we have
$h_{n} = {(0.8)}^{2 n} (1 m)$
$h_{n} = {(0.8)}^{2 n}$

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