Question

A girl riding a bicycle along a straight road with a speed of 5 m/s throws a stone of mass 0.5 kg which has a speed 15 m/s 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 ?

Answer 1

Answer:

Yes the speed of the bicycle changes after the stone is thrown

The change in speed is 4.9 m/s

Explanation:

Mass of the girl and bicycle = 50 kg

Mass of the stone = 0.5 kg

Velocity of the bicycle = 5 m/s

Velocity of the stone with respect to the ground = 15 m/s

Initial momentum of girl+bicycle+stone = $(50+0.5)\times5$

If the change in velocity of the girl with bicycle is v then

From the conservation of linear momentum

Initial momentum = Final momentum

$(50+0.5)\times5=0.5\times15-50v$

$\implies 50.5\times5-0.5\times15=-50v$

$\implies v=-4.9$ m/s

Therefore, the velocity of the girl = 5 - 4.9 = 0.1 m/s