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A boy of mass 50 kg running at 5 m/s jumps on to a 20 kg trolley travelling in the same direction at 1.5 m/s. What is their common velocity?
As given, Mass of the boy, $m_1=50\ kg$
Speed of boy, $u_1=5\ m/s$
Mass of trolley $m_2=20\ kg$
Speed of trolley $u_2=1.5\ m/s$
Combined mass of boy and trolley, $m=m_1+m_2=20+50=70\ kg$
Let the combined velocity be $v$.
According to the law of conservation of momentum
Total momentum before jump$=$Total momentum after the jump
$m_1u_1+m_2u_2=mv$
Or $250+30=70v$
Or $70v=280$
Or $v=\frac{280}{70}$
Or $v=4\ m/s$
Thus, the common velocity is $4\ m/s$.
Updated on: 10-Oct-2022
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