Question

A bullet loses 1/20 of its velocity in passing through a plank.What is the least number of planks required to stop the bullet?

Answer 1

Hey !

Let v be the speed of the bullet incident on the first plank.

Its speed after it passes the plank = 19/20 v

If x is the thickness of the plank, the deceleration a due to resistance of plank is given by,

           (19/20)² v² - v² = 2ax

=> 2ax = -39/400 v²

Let the bullet is stopped after passing through n such planks. Then the distance covered by bullet is x

      => 0 - (19/20)² v² = 2anx

     => -(19/20)v² = n × -39/400 v²

     => n = 361/39 = 9.25 ≈ 9

GOOD LUCK !