Question

if a body loses half of its velocity on penetrating3 cm in a wooden block, then how much will it penetrate more before coming 2 rest ??

Answer 1

it will penetrate 1cm more before coming to rest

in first case

initial velocity(u)=v , final velocity(v)=v/2 ;distance covered(s)=3cm

we know 2as=v2-u2  

2*a*3=(v/2)2 - v2

a= -v2 / 8

in second case

initial velocity(u)=v , final velocity(v)=o ;distance covered(s)=we hav to find out

here we know acceleration=-v2 / 8

2as=v2-u2  

2*(v2 / 8)*s=(0)2 - v2

on solving we get

s=4cm

but it had already pnetrated 3 cm thrfore it will pertratr 1 cm more to come to rest