Question

Mass A has an initial velocity of 53 m/s in the +x-direction. Mass B is two times more massive than mass A and has an initial velocity of 53 m/s in the −x-direction. If the two masses have an elastic collision, what will be the final velocities (in m/s) of the masses after the collision? (Indicate the direction with the sign of your answer.) mass A m/s mass B m/s

Answer 1

In an elastic collision both momentum and kinetic energy is conserved.

We assume A and B has masses m₁, m₂, and velocities u₁, u₂ before collision, v₁, v₂ after collision.

So according to the conservation of momentum,

According to the conservation of kinetic energy,

Solving these two equations for v₁ and v₂ we get,

Now putting u₁ = 53 , u₂ = -53 and m2 = 2m₁,

We get,

So A will have a speed of 88.33m/s in the -X axis and B will have 17.66m/s in the +X axis.