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Grade: 12
        
A bullet loses 1/20 of its velocity in passing through a plank.The least number of planks needed to stop the bullet is...
8 months ago

Answers : (1)

Arun
13976 Points
							
Dear Vaishnavi
 
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
Ans: 11

 

Regards

Arun (askIITians forum expert)

8 months ago
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