A body falling on the ground from a height of `10m` rebounds to a height of `2.5m`. Calculate (i) the percentage loss of kinetic energy of the body during its collision with the ground. (ii) ratio of the velocities of the body just before and just after collision.
Here,`h_(1)=10m, h_(2)=2.5m`
Let `upsilon_(1)` be the velocity of the body just before collision with the ground and `upsilon_(2)` be the velocity of the body just after collision.
`:. (1)/(2)m upsilon_(1)^(2)=mgh_(1)` and `(1)/(2)m upsilon_(2)^(2)=mgh_(2)`
Dividing, we get
`(upsilon_(1)^(2))/(upsilon_(2)^(2))=(h_(1))/(h_(2))=(10)/(2.5)=4,` `:. (upsilon_(1))/(upsilon_(2))=2`
`%` age loss in KE`=(K_(1)-K_(2))/(K_(1))xx100`
`=(mg(h_(1)-h_(2)))/(mgh_(1))xx100=((10-2.5))/(10)xx100=75%`