A bullet leaving the muzzle of a rifle barrel with a velocity v penetrates a plank and loses one-fifth of its velocity. It then strikes second plank, which it just penetrates through. Find the ratio of the thickness of the planks, supposing the average resistance to the penetration is same in both the cases.

A bullet leaving the muzzle of a rifle barrel with a velocity v penetr

1.	A bullet leaving the muzzle of a rifle barrel with a velocity v penetrates a plank and loses one-fifth of its velocity. It then strikes second plank, which it just penetrates through. Find the ratio of the thickness of the planks, supposing the average resistance to the penetration is same in both the cases.
Answer» Let R be the resistance force offered by the planks, `t_1` be the thickness of first plank, and `t_2` be the thickness of second plank. For first plank: Loss in KE=work against resistance `1/2mv^2-1/2m(4/5v)^2=Rtimplies1/2mv^2(9/25)=Rt_1` (i) For second plank: `1/2m(4/5v)^2-0=Rt_2implies1/2mv^2(16/25)=Rt_2` (ii) Dividing Eq. (i) by Eq. (ii), we get `t_1/t_2=9/16`

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