A ship's caption sets a course due south at 11 mph. The water is moving at 7 mph due east. What is the actual velocity of the ship, and in what direction is it traveling?
A) 13.0 mph; 32.5° east due south
B) 170 mph; 57.5° east due south
C) 18.0 mph; 39.5° east due south
D) no solution

Question

Quizplus · Accepted Answer

The actual velocity of the ship can be found using the Pythagorean theorem, as the ship's southward velocity and the water's eastward velocity form a right-angled triangle. The magnitude of the velocity is $\sqrt{11^2 + 7^2} = \sqrt{121 + 49} = \sqrt{170} = 13.0$ mph. The direction can be found using the tangent of the angle, $\tan(\theta) = \frac{7}{11}$, which gives $\theta \approx 32.5^\circ$ east of south.

A Ship's Caption Sets a Course Due South at 11