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 ?
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 ?
Mass of girl bicycle $=50 \mathrm{~kg}$
mass of stone $=0.5 \mathrm{~kg}$
Total mass of system (girl + bicycle + stone)
$=50+0.5$
$=50.5 \mathrm{~kg}$
Velocity of bicycle $u_{1}=5 \mathrm{~m} / \mathrm{s}$, Mass of stone $\mathrm{m}_{2}=0.5 \mathrm{~kg}$ Velocity of stone $u_{2}=15 \mathrm{~m} / \mathrm{s}$, Mass of girl and bicycle $m=50 \mathrm{~kg}$ Yes, the speed of the bicycle will change after the stone is thrown. Let after throwing the stone $v \mathrm{~m} / \mathrm{s}$ speed of bicycle By law of conservation of linear momentum,
$m_{1} u_{1}=m_{2} u_{2}+m v$
$\therefore 50.5 \times 5=0.5 \times 15+50 \times v$
$\therefore 252.5-7.5=50 v$ $\therefore v=\frac{245.0}{50}$ $\therefore v=4.9 \mathrm{~m} / \mathrm{s}$ Change in speed $=5-4.9=0.1 \mathrm{~m} / \mathrm{s}$
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