Question

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Answer 1

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



Final Answer:11
Case 1:
In case of only one plank:
Assuming there is constant retardation by each plank.
See pic 1:
Let the thickness is 'd' and initial velocity of rifle be 'u'.
Final velocity,v = 19u/20.
Initial velocity, v(0) = u.
acceleration, a = a (say)

By applying Newtons equation of motion.
v^2-u^2= 2aS
=> (19u/20)^2-u^2=2ad. ------(1)

Case :2
Let there be 'n' number of planks.
Then, To stop the bullet.
Final velocity, v = 0
Initial velocity, v(0) = u
Total displacement, s = nd

Applying Newtons equation of motion.
0^2-(u)^2 = 2a(nd )-------(2)

By dividing eq. 2) by 1),

we get,
n = u^2 /(u^2-(19u/20)^2) = 400/39 = 10.25
Since,
more than 10 planks are required to stop the rifle.
=> 11 planks are required to stop the rifle.