Question

A ball with a mass of `4 kg` and velocity of `1 m/s` collides with a second ball with a mass of `5 kg` and velocity of `- 8 m/s`. If `25%` of the kinetic energy is lost, what are the final velocities of the balls?

Answer 1

Approximately 5.20 meters per second

Explanation:

Kinetic energy formula is `E= 0.5*m*v*v`
m is for mass (kg) and v is for velocity (m/s).
The first ball's kinetic energy is `E1=2 kg*m*m/(s*s)`
The second ball's kinetic energy is `E2=160 kg*m*m/(s*s)`
Total energy when they collide is `E=162 kg*m*m/(s*s)`

However only 75% of this value is saved after collision of these balls. In other words total kinetic energy after collision is `121.5 kg*m*m/(s*s)`

Final mass of these balls `9 kg` but what is final velocity?

`121.5 kg*m*m/(s*s) = 0.5*9*v*v`

`27 = v*v`

`5.196 = v` (as m/s).

This is the answer of the velocity of the final ball (9 kg). It moves similar to the direction of the second ball with a lower speed.