A child in a boat throws a 5.90 kg package out horizontally with a speed of 10.0 m/s?

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JessicaFord

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Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 28.0 kg and that of the boat is 45.0 kg. Ignore water resistance.
 
(28 + 45) = 73kg.
(5.9 x 10) = 59kg/m/s.
(59/73) = imparted velocity of 0.808m/sec.
 
Beforehand, the total momentum is zero, since everything is at rest.

Afterwards:
Momentum of package: 5.9*10 = 59.0 kg m/s
Momentum of boat: (45+28)v = 73v kg m/s (letting v be the velocity of the boat)

So by the Law of conservation of linear moment:
0 = 59 + 73v
v = -59/73 = -0.81 m/s

The minus sign is because the boat moves in the opposite direction to the package (which was expected) whose velocity we took to be positive.

So the final speed of the boat and the child is 0.81 m/s !!!
 
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