Question

A person 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 3.6 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?

Answer 1

The direction of motion of the person relative to the water is 16.7° north of east.

Why?

We can solve the problem by applying the Pitagorean Theorem, where the first speed (to the north) and the second speed (to the east) corresponds to two legs of the right triangle formed with them. (north and east directions are perpendicular each other)

We can calculate the angle that give the direction using the following formula:

$Tan(\alpha)=\frac{NorthSpeed}{EastSpeed}\\\\Tan(\alpha)^{-1}=Tan(\frac{NorthSpeed}{EastSpeed})^{-1}\\\\\alpha=Tan(\frac{NorthSpeed}{EastSpeed})^{-1}$

Now, substituting the given information we have:

$alpha=Tan(\frac{NorthSpeed}{EastSpeed})^{-1}$

$\alpha =Tan(\frac{3.6\frac{m}{s} }{12\frac{m}{s} })^{-1}\\\\\alpha =Tan(0.3)^{-1}=16.69\°(North-East)=16.7\°(North-East)$

Hence, we have that the direction of motion of the person relative to the water is 16.7° north of east.

Have a nice day!