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

Here, total mass of giral cycle and stone `m_(1) = 50kg`
initial speed , ` u_(1) = 5 m//s, ` mass of stone ` m_(2) = 0.5 kg` velocity of stone, `u_(2) = 15m//s`
If upsilon is speed of girl and cycle (of mass m = 50kg) after throwing the stone, then applying principle of conservation of linear momentum, we get
` m_(1) u_(1) =m_(2) u_(2) + m upsilon`
`m upsilon= m_(1) u_(2) -m_(2)u_(2)`
`50 upsilon= 50.5 xx 5- 0.5 xx 15 = 252.5 - 7.5 = 245 `
`upsilon=(245)/(50) = 4.9 m//s `
change in speed `= 5 - 4.9 =0.1 m//s` .