Question

You are walking north on a barge that is traveling north on a river that flows south. A second person is standing still on the barge. A third person is floating on the surface of the water, meaning that they are not propelling themselves. A fourth person is standing still on the bank of the river. In the reference frame of which person is the magnitude of your velocity greatest?

Answer 1

let the velocity of the first person be V1 towards North on the Barge.

Let the velocity of the Barge is V2 towards North.

Then the speed of the person with respect to the ground is V1 + V2 North

The second person is on Barge. Hence with respect to second person, the first person speed is V2 North.

The third person is floating on water surface. As water is flowing towards South, let its velocity is V3.

Then with respect to third person, the speed of the first person is V1 + V2 + V3 North.

The fourth person is standing on ground. Hence with respect to him, the speed of the first person is V1 + V2 North.

From the above values, the magnitude of velocity is greatest from the reference frame of third person.