Particle one of mass m initially moves to the right at v.Particle two of mass 2m is initially at rest.After they undergo an elastic collision,particle one moves directly down.What is the final speed of particle two?
A)0.577 v
B)0.707 v
C)0.500 v
D)0.250 v
E)0.764 v

Question

Quizplus · Accepted Answer

Momentum is conserved in the x direction, so the total momentum before the collision is mv to the right, and the total momentum after the collision is 2mv to the left. Therefore, the x component of the velocity of particle two after the collision is -v/2.Kinetic energy is also conserved in the collision, so the total kinetic energy before the collision is 1/2 mv^2, and the total kinetic energy after the collision is 1/2 (2m)v^2/4 + 1/2 mv^2/4 = 3/4 mv^2. Therefore, the speed of particle two after the collision is sqrt(3/4) v = 0.577 v.

Particle One of Mass M Initially Moves to the Right