What is the relative velocity of a man in a boat with respect to the river and the earth?

Question

A river flows due south with a speed of 2.00m/s . A man steers a motorboat across the river; his velocity relative to the water is 4.20m/s due east. The river is 800m wide.
What is the magnitude of his velocity relative to the earth? What is the direction of his velocity relative to the earth? How much time is required for the man to cross the river?

Answer 1

With respect to the Earth, there are two components of velocity
-2.00 m/s (South)
and 4.2 m/s (East)
the magnitude is
sqrt(4+4.2^2)

The direction is
ATAN(2/4.2) South of East

To cross to the opposite bank will be
800=4.2*t
t=800/4.2

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