Question

A raft of 180 kg carries two swimmers with masses of 50 kg and 80 kg. The raft is initially floating at rest. The two swimmers simultaneously dive off opposite ends of the raft, each would a horizontal velocity of 3 m/s. With what velocity and in what direction does the raft start to move?

Answer 1

Answer:

v=0.5m/s

Explanation:

Given a raft of 180kg, and two simmers of 50kg and 80kg:

The two rafts have an initial velocity of zero:

$\bigtriangleup P_{raft}+\bigtriangleup P_{50}+\bigtriangleup P_{80}=0\\\\m_R\bigtriangleup v_R+m_{50}\bigtriangleup v_{50}+m_{80}\bigtriangleup v_{80}=0\\\\m_R\bigtriangleup v_R=-m_{50}\bigtriangleup v_{50}-m_{80}\bigtriangleup v_{80}\\\\\bigtriangleup v_R=\frac{-m_{50}\bigtriangleup v_{50}-m_{80}\bigtriangleup v_{80}}{m_R}\\\\\bigtriangleup v_R=\frac{-(50kg\times3m/s+80kg\times-3m/s)}{180kg}\\\\\bigtriangleup v_R=0.5m/s$

Hence, the raft starts moving with avelocity of 0.5m/s

-The raft will continue moving in the direction it was initially moving. The raft has a larger mass than the combined mass of the two swimmers, by law of momentum conservation, it's change in velocity will be negligible.