Question

One ship is 1 mile north of a certain pier and is travelling N 30' E a rate of 3 miles per hour. Another ship is 3/4 mile east of the pier and is travelling east at a rate of 7 miles per hour. How fast are the ships seperating?

Answer 1

We will call the east of pier A and the ship north of the pier B. By convention we will let North-South be the vertical direction (y's) with Northerly being positive and the East-West will be horizontal with Easterly being positive. Now, let's break the ship B's speed into it's components. So\[ \frac{dx_B}{dt}=3/2mph\]and \[ \frac{dy_B}{dt}=\frac{3\sqrt{3}}{2}mph\]. While \[ \frac{dx_A}{dt}=7\] and \[ \frac{dx_A}{dt}=0\].