A child in a boat throws a 5.80-kg package out horizontally with a speed of 10.0

Question

A child in a boat throws a 5.80-kg package out horizontally with a speed of 10.0 m/s. The mass of the child is 23.0kg and the mass of the boat is 35.0kg.

Calculate the velocity of the boat immediately after, assuming it was initially at rest.

Express your answer to three significant figures and include the appropriate units. Enter positive value if the direction of the force is in the direction of the velocity of the box and negative value if the direction of the force is in the direction opposite to the velocity of the box.

Explanation / Answer

Use the law of conservation of momentum, i.e.,

Initial momentum = Final momentum

McVc + MbVb + MpVp = McVf + MbVf

where

Mc = mass of the child = 23 kg (given)
Vc = initial velocity of the child = 0
Mb = mass of the boat = 35 kg. (given)
Vb = initial velocity of the boat = 0
Mp = mass of the package = 5.8 kg (given)
Vp = velocity of package = 10 m/sec (given)
Vf = final velocity

NOTE -- the final velocity of the child and the boat are the same since the child is still on the boat after the package was thrown

Substituting appropriate values,

0 + 0 + (5.80)(10) = 23(Vf) + 35(Vf)

Simplifying and rearranging,

58(Vf) = 58

Vf = 1.0 m/sec.

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