First slide

Coefficient of restitution

Question

A metallic sphere is dropped from a height 20 m above the horizontal hard floor. The sphere strikes the floor in turn and rebounds several times. If the dropped sphere makes 2 nd impact with floor after a time interval of 4 seconds from the time of dropping, the distance travelled by the sphere during that time is $(g = 10 {ms}^{- 2})$

Moderate

A

30 m
B

35 m
C

40 m
D

45 m

Solution

$\sqrt{\frac{2 h}{g}} (1 + 2 e) = 4 \Rightarrow e = \frac{1}{2} (4 \sqrt{\frac{g}{2 h}} - 1) = 0.5$
$and S = h + 2 h_{1} = h + 2 e^{2} h = 20 + 2 \times 0.25 \times 20 = 30 m$

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