A girl riding 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 15 `ms^(-1)` with respect to the ground along her direction of motion. The mass of the girl and bicycle is 50 kg. Does the speed of the bicycle change after the stone is thrown ? What is the change in speed, if so

Explanation

Mass of girl bicycle =50 kg
Total mass of system (girl + bicycle + stone )
velocity of bicycle `mu_(1) 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 will change after the stone is thrown.
Let after throwing the stone `vm//s` speed of bicycle
By 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`
`v= (245.0)/( 50)`
`v= 4.9 m//s`
Change in speed =5- 4.9 =0.1 m//s`