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Similarity of Triangles

A 50.0-kg boy...

Question

A 50.0-kg boy runs at a speed of 10.0 m/s and jumps onto a cart as shown in the figure. The cart is initially at rest. If the speed of the cart with the boy on it is 2.50 m/s, what is the mass of the cart?

A

260 kg

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B

200 kg

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C

175 kg

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D

150 kg

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Solution

The correct option is D
150 kg

$m_{1 i} v_{1 i} + m_{2 i} v_{2 i} = (m_{1} + m_{2}) v_{f}$

$\frac{(m_{1 i} v_{1 i} + m_{2 i} v_{2 i})}{v_{f}} = (m_{1} + m_{2})$

$\frac{(50 \times 10 + 0)}{2.5} = (m_{1} + m_{2})$

$200 = (50 + m_{2})$

$m_{2} = 150 k g$

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