Question

Question #a4d65

Answer 1

Because of the Momentum Conservation Law, sum of momentum of all objects participating in the action should be the same BEFORE and AFTER the action.

Explanation:

Momentum of a moving object is a product of its mass by its velocity (a vector directed towards the direction of the movement).

Let's ignore the water under a boat because its affect is minimal comparing with other forces participating in the movement, the friction between the boat and the water can be ignored for our purposes.

Before the jump a boat and a man are at rest, so their combined momentum is zero. Therefore, their combined momentum should be zero after the jump - this is the Momentum Conservation Law of Physics.

After the jump the momentum of a man (mass times velocity - vector) is not zero. Therefore, to preserve the combined momentum to be zero, the boat must move in the opposite direction with some velocity. The equation that determines this process is:
`M_m*V_m + M_b*V_b = 0`
where index `m` refers to a man and index `b` refers to a boat.
Notice that masses `M_m` and `M_b` are scalars, velocities `V_m` and `V_b` are vectors.

From the above equation, that reflects the fact that combined momentum should stay at zero, follows:
`V_b = -M_m/M_b * V_m`
The 'minus' sign indicates that the direction of a boat is opposite to the direction of a jumping man.

As seen from the last expression, the greater the mass of a boat `M_b` - the slower its movement. That's why a small light boat, when a man jumps from it, moves backward faster than a big heavy boat. And, if you jump from an ocean crew ship, you do not observe it moving at all.