A boy of mass $50 k g$ mass runs and jumps onto a stationary cart of mass $80 k g$ . After landing, he moves along with the cart at a speed of $0.4 m s^{- 1}$ . What is the initial velocity of the boy?

150 kgm/s

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20 kgm/s

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50 kgm/s

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100 kgm/s

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Solution

The correct option is D 100 kgm/s
Given,mass of the boy, $m_{1} = 50 k g$
Mass of cart, $m_{2} = 80 k g$
Initial velocity of cart, $u_{2} = 0$
Final velocity of cart = Final velocity of boy, $v = 0.8 m s^{- 1}$
Let initial velocity of boy be $u_{1}$ .
Initial momentum of boy $= m_{1} u_{1} = 50 u_{1}$
Initial momentum of cart $= 0$ (initially at rest)
Final momentum of boy $= m_{1} v = 50 \times 0.8 = 40 k g m s^{- 1}$
Final momentum of cart $= m_{2} v = 80 \times 0.8 = 64 k g m s^{- 1}$

By law of conservation of momentum:
Total initial momentum = Total final momentum
$m_{1} u_{1} + 0 = m_{1} v + m_{2} v \Rightarrow u_{1} = \frac{(m_{1} + m_{2}) v}{50} = \frac{130 \times 0.8}{50} \Rightarrow u_{1} = 2.08 m s^{- 1}$
Therefore, the initial velocity of the boy is $2.08 m s^{- 1}$

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A boy of mass 50 kg mass runs and jumps onto a stationary cart of mass 80 kg. After landing, he moves along with the cart at a speed of 0.4 ms−1. What is the initial velocity of the boy?

A boy of mass $50 k g$ mass runs and jumps onto a stationary cart of mass $80 k g$ . After landing, he moves along with the cart at a speed of $0.4 m s^{- 1}$ . What is the initial velocity of the boy?