First slide

Work

Question

If a body looses half of its velocity on penetrating 3 cm in a wooden block, then how much will it penetrate more before coming to rest

Moderate

A

1 cm
B

2 cm
C

3 cm
D

4 cm

Solution

For first condition
Initial velocity = u, Final velocity = u/2, s = 3 cm
From $v^{2} = u^{2} - 2 as \Rightarrow {(\frac{u}{2})}^{2} = u^{2} - 2 as \Rightarrow a = \frac{3 u^{2}}{8 s}$
Second condition
Initial velocity = u/2, Final velocity = 0
From $v^{2} = u^{2} - 2 ax \Rightarrow 0 = \frac{u^{2}}{4} - 2 ax$
$∴ x = \frac{u^{2}}{4 \times 2 a} = \frac{u^{2} \times 8 s}{4 \times 2 \times 3 u^{2}} = s / 3 = 1 cm$

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