Aperson on a cruise ship is doing laps on the promenade deck. on one portion of the track the person is moving north with a speed of 4.1 m/s relative to the ship. the ship moves east with a speed of 12 m/s relative to the water. part a what is the direction of motion of the person relative to the water?

Relative to the water, the person is moving north at 4.1 m/s and east at 12 m/s. This means these are the two components of its velocity (we can think north as y-direction and east as x-direction), so the  angle between the direction of its velocity with respect to the water is given by

from which 

in the north-east direction.