A river that is flowing due west is crossed by a boat travelling from the south bank to the north bank. The boat can travel at 30 m/s in still water and the river is moving at 10 m/s.
The boat's velocity relative to the water can be found using vector addition. Let's designate the boat's velocity as Vb, which is 30 m/s due west, and the river's velocity as Vr, which is 10 m/s due west. Since they are both in the same direction, we can simply add them together:
Vw = Vb + Vr
Vw = 30 m/s + 10 m/s = 40 m/s
So the boat's velocity relative to the water is 40 m/s due west.