Question

a motor boat heads due east at 11m/s relative to the water across a river that flows due north at 5.0m/s. What is the velocity of the motorboat with respect to the shore?

Answer 1

An observer standing on the shore would be able to see the full motion of the boat due to both the boat moving east and the water pushing the boat to the north.

So we need the vector sum of the velocities to find what the observer sees.



Pythagorean theorem: a^2 + b^2 = c^2
c = sqrt(5^2 + 11^2) = sqrt(25 + 121) = sqrt(146) = 12.1 m/s

Find the angle using any of the trig functions. Let's just use tangent.
angle = arctan(5/11) = 24.4 degrees

So the velocity seen by the observer on shore is 12.1 m/s @ 24.4 degrees north of east.