Question

A bullet loses 1/15th of its initial velocity while passing through a plank. Find the number of planks required to stop the bullet?​

Answer 1

hello,

A rifle bullets loses 1/20 of its velocity in passing through a plank exerts a constant retarding force the least no. of such planks required just to stop the bullet.

Let the thickness of one plank = d

and the acceleration provided by the plank = a

v^2 = vo^2 + 2ad

If n planks are required to stop the bullet, then

0^2 = vo^2 + 2a*nd

2and = -vo^2

n = vo^2/(-2ad) -----------------(1)

v = vo - vo/20 = 19 vo/20 in passing through one plank

(19 vo/20)^2 = vo^2 + 2ad

361/400 * vo^2 = vo^2 + 2ad

-2ad = vo^2(1 - 361/400)

-2ad = vo^2 * 39/400

Substituting this value of -2ad into equation (1):

n = vo^2/(vo^2 * 39/400) = 400/39

The minimum number of planks needed = smallest integer greater than 400/39 = 11

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