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

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

Grade:11

1 Answers

Arun
25750 Points
3 years ago
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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