A river flows south with a velocity of 2m/s. A man steers his boat across the river with a velocity of 4m/s to east relative to the river.

Question

Find the orignal velocity of the boat

MY SOLUTION:

Let’s assume coordinate axes along the conventional directions, where +x is in east and +y is north (although it’s relatively unimportant)

Since the relative velocity of boat wrt to river is 4j and $$V_{AB}=V_A-V_B$$ So $$4j=V+2i$$where v is the actual velocity of the boat. $$V=4j-2i$$ $$V=\sqrt{20}$$ $$V=2\sqrt5$$

The answer given is $4\sqrt5$, which I highly doubt is wrong, but I needed to confirm it nonetheless. I know it’s an extremely simple question, but I needed to get it verified.

Thank a lot!