Question

A croquet player hits a wooden croquet ball so that it strikes an identical ball at rest. Just before the collision, the moving ball had a velocity of v0 to the right. After the collision, both balls follow trajectories that make the same angle, θ with (but on opposite sides of the originally moving ball’s initial velocity. What are the speeds v1 and v2 after the collision and how much kinetic energy is lost in the collision? Your answers should be in terms of v0 and θ.

Answer 1

Let the initial velocity direction be along x axis, and final velocity of the balls make angle θ above and below the x axis.

momentum conservation along y axis , mv1 sin θ = mv2 sin θ,

so v1 = v2

now momentum conservation in x axis,

mv0 = mv1 cos θ + mv2 cos θ

v0 = v1 cos θ +v2 cos θ, here v1 = v2

so v0 = 2v1 cos θ

v1 = v0/[2 cos θ]

v2 = v0/[2 cos θ]

Kinetic energy lost = 0.5mv0^2 - 0.5mv1^2 - 0.5mv2^2

= 0.5mv0^2 - mv0^2/[4 cos^2 θ]

= 0.5mv0^2 *(1- 1/(2 cos^2 θ))