A 60 kg canoeist jumps into his canoe from the deck (after getting a running start) with speed s. With what speed does the canoe weighing 30 kg move.

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justaguide | College Teacher | (Level 2) Distinguished Educator

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The canoe and the canoeist can be considered to be a closed system. The total momentum of a closed system is conserved.

Initially, the canoeist is moving at a velocity equal to s. The mass of the canoeist is 60 kg. The canoe is at rest and the mass of the canoe is 30 kg. The initial momentum of the canoeist is 60*s kg*m/s. The initial momentum of the canoe is 0. When the canoeist jumps on to the canoe, the canoe and the canoeist move at the same velocity. Let this be equal to s'.

The law of conservation of momentum gives: s'(30+60) = 60*s + 0

=> 90s' = 60s

=> s' = (60/90)*s

=> s' = (2/3)*s

The speed with which the canoe weighing 30 kg moves after the canoeist weighing 60 kg and moving at s m/s jumps into it is (2/3)*s