Question

A body loses half of its velocity on penetrating 6cm in a wooden block . How much will it penetrate more before coming to rest?

a)1cm

b)2cm

c)3cm

d)4cm.

Answer 1

Let the initial velocity be u and acceleration be a. Its velocity becomes u/2 after penetrating 6 cm or 0.06 m.

So,

(u/2)² = u² + 2(a)(0.06)

=> u²/4 = u² + 0.12a

=> a = -u²/0.16

Now, let it penetrate total ‘x’ and come to rest.

So, 0² = u² + 2ax

=> 0 = u² – 2u²x/0.16

=> x = 0.08= 8 cm

Hence, before coming to rest the body penetrates further by 8 – 6 = 2 cm.