A bullet loses ` 1//2th1 of its velocity is passing through a plank. What is the least number of planks required to stop the bullet ?

Explanation

Let (u) the initial velocity of butter and (a) be the retardation of the bullet while passing through a plank. Velcoty of bullet after passing through a plank is
` u =u - u//20 = 19 u //20`
Taking motion of bullet through one pland and using the relation, `v^2 =u^2 = 2 a S, we have
` (19 u //20 )^2 -2 aS1
or ` `2 aS= u^2 - (36 1//400) u^2 = 39 u^2 //400`
Let (n) number of plands be required to stop the bullet. Taking motion of bullert through (n) planks, we have
` ` u =u, v= 0, S= nS. a=-a, then`
` O^2 =u^2 -2 a Sn`
or ` n= u^2 / (2 a S) = u^2 /((39u^2//400) = (4000/(39) ~~ 11`.