Question

Two balls of equal mass collide in a perfectly elastic collision. Ball A moves to the right at

10 m/s. Ball B moves to the left at 5 m/s. After the collision, Ball B moves to the right at
3 m/s. What is the velocity of Ball A after the collision?

Answer 1

After a perfectly elastic collision, where Ball A moves right at 10 m/s and Ball B left at 5 m/s, with Ball B ending up moving right at 3 m/s post-collision, Ball A will have a final velocity of 2 m/s to the right.

Step-by-step explanation:

In a perfectly elastic collision between two balls (A and B) of equal mass, where Ball A has a velocity of 10 m/s to the right and Ball B has a velocity of 5 m/s to the left prior to the collision, the conservation of momentum and kinetic energy must be observed. After the collision, Ball B moves to the right with a velocity of 3 m/s. To find Ball A’s final velocity after the collision, we can set up the equation for the conservation of momentum because the masses are equal and momentum is conserved:

mA * vA_initial + mB * vB_initial = mA * vA_final + mB * vB_final

Since the masses are equal and can be canceled out, we simplify:

10 m/s + (-5 m/s) = vA_final + 3 m/s

Solving for vA_final gives us:

vA_final = 10 m/s - 5 m/s - 3 m/s

vA_final = 2 m/s

Therefore, after the collision, Ball A will have a velocity of 2 m/s to the right.