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A rifle loses 1/20 th of its velocity in passing through a plank .The least number of such planks required just to stop the bullet are

A rifle loses 1/20th of its velocity in passing through a plank.The least number of such planks required just to stop the bullet are                

Grade:10

1 Answers

Aarti Gupta
askIITians Faculty 300 Points
7 years ago
Let us suppose that thickness of each planck be taken as ‘t’.Also suppose ‘n’ no. of plancks are required to stop the bullet.
uniform retardation = a
Initial velocity of rifle = u
Now,after piercing in the first planck,final vaelocity will be
u – u/20 = 19u
20
We know that,
v2 = u2 + 2as
or,
v2 – u2 = 2at
(19u/20)2 – u2 = 2at
or, 2at = – 39u2/400 --------- eq.(1)
When rifle passes through such ‘n’ no. of plancks its final velocity will be 0.
0 – (19u/20)2 = 2ant ------------ eq.(2)
substitute the value of 2at from eq.1 in eq.2 we get,
0 – [19u/20]2 = n* – 39u2/400

or, n = – 400/--39u2[19u/20 ]2

n = 9.25 or it is taken as 10

therefore,total no. of such plancks will be 10 + 1 = 11

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