A girl ridding a bicycle along a straight road with a speed of `5 ms^(-1)` throws a stone of mass 0.5 kg which has a speed of `15ms^(-1)` with respect to the ground along her direction of motion. The mass of the girl and bicycle is ` 5 kg` . Does the speed of the bicycle change after the stone is thrown ? What is the change in speed, if so ?

Explanation

Given , total mass of girl , bicycle and stone = `m_(1) = (50 + 0.5)` kg = `50.5` kg .
Velocity of bicycle `u_(1) = 5` m/s . Mass of stone `m_(2) = 0.5` kg
Velocity of stone `u_(2) ` = 15 m/s , Mass of girl and bicycle m = 50 kg
Yes , the speed of the bicycle changes after the stone is thrown .
Let after throwing the stone the speed of bicycle be v m/s
According to law of conservation of linear momentum .
`m_(1) u_(1) = m_(2) u_(2) + mv`
`50.5 xx 5 = 0.5 xx 15 + 50 xx v `
`252.5 - 7.5 = 50 v `
or `" " v = (245.0)/(50)`
v = 4.9 m/s
Change in speed = 5- 4.9 = 0.1 m/s