Question

A rifle bullets loses 1/20 of its velocity in passing through a plank exerts a constant retarding force the least no. of such planks required just to stop the bullet.

Answer 1

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.

Answer 2

⛦Hҽɾҽ ɿʂ ү๏υɾ Aɳʂฬҽɾ⚑
▬▬▬▬▬▬▬▬▬▬▬▬☟

➧ No. of planks
➾ n² / 2n - 1

➧ Where n is loss in velocity.

➧ There your answer will not consume time as time is marks in such exam,

➾ 20² / 2 × 20 - 1
➾ 10.25
➾ 11 planks ...✔

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Thanks...✊