A child in a boat throws a 6-kg package horizontally to the right with a speed of 8 m/s. Assume the boat is initially at rest, the mass of the child is 30 kg and the mass of the boat
is 60 kg. Assume no air resistance. Calculate the velocity of the boat with the child.

0.5 m/s

Explanation:

Using conservation of momentum, P1=P2, the system starts off with zero momentum as nothing is moving. But in the second part of the equation(P2) the child throws the package to the right. By Newton's third law, the child and the boat should move to the left. Plugging in what we know, 0= -90v + 6kg*8m/s. Solving for v you will get 0.5 meters per second. The mass is 90kg as that the is mass of the child and boat combined. I also made it negative as the boat and child move left (I designated this as the negative direction) and the package's momentum is positive as it is moving to the right.

total distance travelled = 60 miles

total time taken =1.5 hours

average speed = total distance / total time

60 / 1.5

= 40

therefore, average speed = 40 m/h

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where are the vectors ?