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Relative Motion in 1D

Figure shows ...

Question

Figure shows a Yacht of mass 400 kg with three decks When the engine if Yacht is off four men A, B, C and D ( $m_{A} = 100 k g, m_{B} = 120 k g, m_{C} = 80 k g a n d m_{D} = 100 k g$ ) started running on different decks with constant horizontal velocities relative to yacht which are marked in figure All the velocity vectors are collinear Due to this Yacht also started moving What is the speed in m/s with Yacth moves

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Solution

Velocity of center of mass = 0
let velocity of yatch is v.
$v_{c o m} = \frac{m_{A} v_{A} + m_{B} v_{B} + m_{c} {. v}_{c} + m v}{m_{A} + m_{B} + m_{c} + m} 0 = \frac{100 \times 40 + 120 \times 20 + 80 \times 10 - 100 \times 16 + 400 v}{800} 0 = \frac{10 + 6 + 2 - 4 + v}{2} v + 14 = 0 v = - 14 m / s = 14 m / s$

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m_{A} = 100 k g, m_{B} = 120 k g, m_{C}

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