Question

Question #22770

Answer 1

Let `m` be the mass of bullet and `v` be its initial velocity before it strikes 1st plank of thickness `d`. It loses `1/40th` of its velocity in piercing the 1st plank and the remaining velocity is `v-v/40=(39v)/40`

If the average resisting force acting within plank be F then by law of conservation of energy we can write

`1/2m(v^2-(39v)^2/40^2)=Fxxd`

`=>1/2xxmxx(79v^2)/40^2=Fxxd.....(1)`

If n such planks are required to stop the bullet (that means to gain zero kinetic energy) then

`1/2mv^2=Fxxnxxd`

Dividing (2) by (1) we get

`n=40^2/79=20.25`

As n represents number of planks required to stop the bullet , it should be a whole number just greater than 20.25.

So n should be `=21`