a sailboat is travelling north at 10km/h, relative ti the water. The water is flowing north at 5km/h. What is the velocity of the boat relative to ground?

Question

what is the solution?

Answer 1

v_bw + v_we = v_be Where the subscript bw means "boat with respect to the water. (so in this case, just add the velocities with sign (here both positive)

This works for higher dimensions, but the addition is vectorial.

Another useful relation is "with respect to" can be calculated if you know velocities from a third inertial (constant velocity) frame:

v_ab = v_ac - v_bc (often c is the earth frame, but it doesn't need to be.

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