Question

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

Answer 1

let intial velocity = u cm/s
final velocity after pemtration = u/2 cm/s

s = 3 cm
using third equation we get
2*a*3= (u/2)^2- u^2
6a = u^2/4 - u^2
6a = -3 u^2 / 4
a = - u^2 / 8
now when the body comes in rest then final velocity will be zero
using third equation again
2* ( -u^2 / 8 ) * s = 0- u ^2
s = 4 cm
so after covering 1 more cm it will come in rest

Answer 2

hi freind
here is your answer..
If a body loses half its velocity on penetrating 3cm into a wooden block, then how much more will it penetrate before coming to rest...
Solution-

Suppose the initial velocity is ‘v'

And so the final velocity after covering 3 cm will be v/2

So by equation of motion,

v^2= u^2 +2as

(v/2)^2= v^2 +2as

v^2/4 -v^2= 2as

2as= -3v^2/4

a= -3v^2/4×2s

a= -3v^2/24

a= -v^2/8

Now,

v^2= u^2 + 2as

And the final velocity is zero

0= v^2/4 -2×(v^2/8)×s

s= (v^2/4)/2× v^2/8

So,

s= 1cm

hope you got it

Regards

Thanks

If you liked it mark as brainliest.