A ferry is crossing a river. If the ferry is headed due North with speed of 2.5m/s relative to the water and the river's velocity is 3 m/s to the east, what will the boat's velocity be relative to Earth?

what is sqrt(2.5^2+3^2)?

3.9 m/s

2,6

To determine the velocity of the ferry relative to Earth, we need to combine the velocity of the ferry relative to the water with the velocity of the water relative to Earth.

The velocity of the ferry relative to Earth will have two components: a northward component and an eastward component.

1. Northward Component:
The ferry's velocity relative to the water is given as 2.5 m/s due north. This means that regardless of the river's flow, the ferry will always move directly to the north. Therefore, the northward component of the velocity relative to Earth will also be 2.5 m/s.

2. Eastward Component:
The river's velocity is given as 3 m/s to the east. Since the ferry is crossing the river, the river's flow will affect the ferry's path. To combine the velocity of the ferry relative to the water with the velocity of the water relative to Earth, we add the two velocities together. In this case, we add the eastward component of the river's velocity to the ferry's velocity relative to the water.

So, the eastward component of the ferry's velocity relative to Earth will be 2.5 m/s (ferry's velocity relative to the water) + 3 m/s (river's velocity to the east) = 5.5 m/s to the east.

Therefore, the velocity of the ferry relative to Earth will be 2.5 m/s to the north and 5.5 m/s to the east.