Question

A boy of 50 kg jumps off a boat (30 kg), causing the boat to move to the right at 2.0 m/s. In what direction and at what velocity does the boy move? (Remember to include - to indicate direction if necessary.)

V=____ m/s to the _____

Answer 1

Answer: The boy moves with velocity = 1.2 m/s to the left.

Explanation:

From law of conservation momentum, when there is no net external force acting on the system, the momentum remains conserved.

⇒M u + m u' = M v + m v'

M is the mass of boy = 50 kg

u is its initial velocity = 0

m is the mass of the boat, m = 30 kg

u' is the initial speed of the boat, = 0

v is the final velocity of the boy

v' is the final velocity of the boat = +2.0 m/s

we would consider positive direction towards and negative towards left.

⇒ 0 = 50 v + 30 × 2

⇒ -50 v = 60

⇒ v = - 1.2 m/s (negative sign indicates towards left)

Thus, the boy moves with velocity = 1.2 m/s to the left.

Answer 2

By Newtons Third law this is an action reaction pair of force
So the momentum is the same
30*20=50*x where x is velocity
x= 12m/s
direction is towards left since they act in opposite directions