Question

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

A)1 cm
B)2 cm
C)3 cm
D)4 cm

answer with explanation..​

Answer 1

Solution:

Let the initial velocity of the body be 'u'.

The velocity becomes $\sf{\frac{u}{2}}$ after penetrating 3 cm in the block.

Note: We can calculate the deceleration of the body using this:

$\boxed{\sf{v^{2}= u^{2} +2as}}$

So we get:

$\implies$ u²/4 = u² + 2a × 3

$\implies$ -3u²/4 = 6a

$\implies$ a = -u²/8

Now substituting for 'a',

We get:

$\implies$ v² = u² + 2as

$\implies$ 0 = u² + 2 × (-u²/8) × s

$\implies$ u² = u²s/4

$\implies$ s = 4 cm

Therefore:

The body penetrates 1 cm (4-3=1cm) more before coming to rest.

Correct option: A) 1 cm

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Answered by: Niki Swar, Goa❤️