Calculating an Intercept Course for a Coast Guard Speedboat

[lazyykid]

Homework Statement

A Coast Guard cutter detects an unidentified ship at a distance of 20.0 km in the direction 15.0° east of north. The ship is traveling at 26.0 km/h on a course at 40.0° east of north. The Coast Guard wishes to send a speedboat to intercept and investigate the vessel. (a) If the speedboat travels at 50.0 km/h, in what direction should it head? Express the direction as a compass bearing with respect to due north. (b) Find the time required for the cutter to intercept the ship.

Homework Equations

Ax=Acosθ
Ay=Asinθ
x=V_it+(1/2)at²

The Attempt at a Solution

Honestly, I don't know how to go about drawing this problem up. If some one could help me set this up, I would be able to answer it.

 

[rude man]

At t = 0 assume the cutter is at x = y = 0, so the ship is at what position?

So what is the ship's position for all t > 0? And, assuming an angle θ for the cutter (with North), what is the cutter's position for all t > 0?

Part (b) can wait until you've solved part (a).

 

[Simon Bridge]

Start by sketching out the situation.
Draw the position of the coastguard boat, then the position of the unidentified ship.
Draw a velocity vector for the ship - Draw an indication of where, roughly, the velocity of the speedboat points.

Notice that while the speedboat travels, the unidentified ship also changes position.

You can do this as a relative motion problem or as a speed-displacement problem.