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A bullet loses 1/20 of its velocity after penetrating into a plank. How many planks are required to stop the bullet ?

A bullet loses 1/20 of its velocity after penetrating into a plank. How many planks are required to stop the bullet ?

Grade:11

4 Answers

Prudhvi teja
83 Points
11 years ago

Dear mohammod

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

 

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Prudhvi Teja

 

 


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vikas askiitian expert
509 Points
11 years ago

applying v^2=u^2+2ad  ,here d is the width of plank

 v=u/20 after penetrating 0ne plank

  2ad=399u^2/400 .........eq1 

  for n number of planks total distance after which bullet stops is nd

 again applying v^2=u^2+2adn  and putting v=0

  n=u^2/2ad......eq2

 solving 1and 2 

   n=1

Susharitha
17 Points
3 years ago
The formula is m=n^2÷2n-1Substituting in this we will be getting 400÷39So the answer should be approximately 10Therefore the required number of planks is 10....
Rishi Sharma
askIITians Faculty 646 Points
one year ago
Dear Student,
Please find below the solution to your problem.

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

Thanks and Regards

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