Question

A ball of mass 0.538 kg moving east ( x direction) with a speed of 3.90 m/s collides head-on with a 0.269 kg ball at rest. Assume that the collision is perfectly elastic. What is the final velocity of the first ball after the collision?

1) 2.60 m/s
2) 3.90 m/s
3) 0.269 m/s
4) Cannot be determined

Answer 1

In an elastic collision, both momentum and kinetic energy are conserved. The final velocity of mass B after the collision is -6.0 m/s in the -x-direction.

Step-by-step explanation:

In an elastic collision, both momentum and kinetic energy are conserved.

Using the principle of conservation of momentum, we can calculate the velocity of mass B after the collision. Since Mass A is initially moving with a velocity of 4.0 m/s in the +x-direction, and Mass B is initially moving with a velocity of 8.0 m/s in the -x-direction, the total momentum before the collision is 0.

The velocity of mass B after the collision can be calculated using the equation:

MassA * VelocityA_initial + MassB * VelocityB_initial = MassA * VelocityA_final + MassB * VelocityB_final

Substituting the known values, we get:

4 * 4.0 + 8 * (-8.0) = 4 * 8.0 + 8 * VelocityB_final

16 - 64 = 32 + 8 * VelocityB_final

-48= 8 * VelocityB_final

VelocityB_final = -48/8

VelocityB_final = -6.0 m/s

Therefore, the final velocity of mass B after the collision is -6.0 m/s in the -x-direction.