Question

A ball with a mass of `1 kg` and velocity of `4 m/s` collides with a second ball with a mass of `5 kg` and velocity of `- 7 m/s`. If `20%` of the kinetic energy is lost, what are the final velocities of the balls?

Answer 1

`v_1 = sqrt12.8 m/s`
`v_2 =2 sqrt7 m/s`

Explanation:

Let velocities of two balls after collision be `v_1 and v_2.`

For ball with mass 1 kg,
Kinetic Energy before collision`=1/2 mv^2`
Kinetic Energy before collision`=1/2 xx 1xx16`
Kinetic Energy before collision`=8 J`
Kinetic Energy after collision`=8- 8xx20/100`
Kinetic Energy after collision`=6.4`
So, `1/2 xx 1 xx (v_1)^2 = 6.4`
`(v_1)^2 = 12.8`
`v_1 = sqrt12.8 m/s`

For ball with mass 5 kg,
Kinetic Energy before collision`=1/2 mv^2`
Kinetic Energy before collision`=1/2 xx 5xx-7`
Kinetic Energy before collision`=-17.5 J`
Kinetic Energy after collision`=-17.5+ 17.5xx20/100`
Kinetic Energy after collision`=-14`
So, `1/2 xx 1 xx (v_2)^2 = -14`
`v_2 = sqrt28`
`v_2 =2 sqrt7 m/s`