A 50 kg girl drives horizontally at 2.0m/s in the positive direction from a 200 kg boat initially at rest. What is the recoil velocity of the boat?
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Before dive both girl and boat are in rest, so total momentum of the system is zero.
When girl dive with velocity V then let say boat will move back in opposite direction with speed v. So new momentum of system will be
MgirlV+mboatv
Form law of conservation of momentum
0 = MgirlV + mboatv
v = −MgirlV / mboat = −50 × 2200 = −0.5 m/s
Negative sign shows that boat moves in direction opposite to girl.
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