Object A strikes the stationary object B with a certain give speed u head-on in an elastic collision. The mass of A is fixed, you may only choose the mass of B appropriately for following cases. Then after the collision:

Options

A. For B to have the greatest speed, choose `m_(B) = m_(A)`
B. For B to have the greatest momentum, choose `m_(B) lt lt m_(A)`
C. For B to have the greatest speed, choose `m_(B) lt lt M_(A)`
D. For the maximum fraction of kinetic energy transfer, choose `m_(B) = m_(A)`

Answer

(B, C, D)

Explanation

`m_(A) u = M_(A) v_(A) + M_(B)v_(B)` and `e = 1 = (v_(B) - v_(A))/(u) rArr v_(B) = (2m_(A)u)/(m_(A) + m_(B))`
For `m_(A) gt gt M_(B), v_(B) = 2u`
For `m_(A) = m_(B), v_(B) = u`
For `m_(A) lt lt m_(B), v_(B) = 0`
kinetic energy `K_(B) = (1)/(2)m_(B)v_(B)^(2) = (2m_(B)u^(2))/((1 + (m_(B))/(m_(A)))^(2)`