A bullet, moving with a velocity of 200 `"m.s"^(-1)` can just go through a 4 cm thick plank. What should be the velocity of a bullet for just going through a 10 cm thick identical plank?

Explanation

The retardation (a) should be the same inside both the planks. The final velocity of the bullet in both cases is zero.
Let the initial velocities of the bullet in the two cases be `u_(1)` and `u_(2)` respectively.
Then , `0 = u_(1)^(2)-2as_(1) " ""or", u_(1)^(2) = 2as_(1)`
Similarly, `u_(2)^(2) = 2as_(2)`
`:. " "u_(1)^(2)/(u_(2)^(2))=s_(1)/s_(2)`
or, `" " u_(2) = u_(1) sqrt((s_(2))/s_(1))=200 xxsqrt((10)/(4))`
`= 100sqrt(10) = 316.2 "m.s"^(-1)`.