A bullet flying at a certain speed hits the earthen rampart and enters it to a depth of 10 cm

A bullet flying at a certain speed hits the earthen rampart and enters it to a depth of 10 cm. To what depth will a bullet of the same mass enter, but flying at twice the speed?

Data: h1 (depth; distance traveled) = 10 cm = 0.1 m; V2 (second speed) = 2V1 (initial speed); the resistance of the earth wall is considered constant.

1) We transform the equality obtained from the formula of the work performed: m * V ^ 2/2 = A = Fcopr. * S, whence S = m * V ^ 2 / 2Fcomp.

2) Let’s compose the depth ratio: S2 / S1 = (m * V2 ^ 2 / 2Fcomp.) / (M * V1 ^ 2 / 2Fcomp.) = V2 ^ 2 / V1 ^ 2 = 4V1 ^ 2 / V1 ^ 2 = 4 p …

3) Determine the desired depth of entry of the bullet into the earthen shaft: S2 / S1 = 4 and S2 = 4S1 = 4 * 0.1 = 0.4 m.