Differential Calculus, Related Rates Application.

[Myung]

Homework Statement

A ship moving at 8 mi per hour, Sails W for 2 hours, then turns N 30 E. A search light, placed at the starting point, follows the ship. Find how fast the light is rotating, (a) 3 hours after the start; (b) just after the turn.

Homework Equations

The Attempt at a Solution

http://img35.imageshack.us/img35/4391/screenshot20111009at501.jpg

This is the image that I have constructed.

I'm stuck at this diagram, I don't know what will be my working equation any tips guys?

 

[Myung]

*bump*

 

[chiro]

Have you thought about using polar co-ordinates?

 

[Myung]

Have you thought about using polar co-ordinates?

What about polar coordinates please elaborate :(

 

[chiro]

What about polar coordinates please elaborate :(

Well polar co-ordinates are basically a different kind of co-ordinate system to the Cartesian based system.

With standard Cartesian systems you have (x,y) or (x,y,z) and so on where each is orthogonal to one another (if you're not familiar with orthogonality, think right angles to each other).

Polar co-ordinates represent points using length and the appropriate angle made. For example in 2D space, your polar representation is given by two parameters r (The length of the point from the origin) and theta (the angle made between the positive x-axis).

My suggestion is you find the polar co-ordinate representation of your system and then using that find the rate of change for your angle theta.

 

[HallsofIvy]

Personally, I wouldn't use polar coordinates. Set up a coordinate system so that the origin is at the search light, the positive x-axis is west and the positive y-axis is south. For the first two hours, the ships path is just the positive x-axis, x= 8t with xy units in miles, t in hours. At the time of its turn, it is at (16, 0). After its turn it is moving with x= 16+ 8 cos(30)t, y= 8 sin(30)t
The search light will be aimed at angle $\theta$ so that $tan(\theta)= y/x$. Differentiate that, with respect to t, to find the rate at which the searchlight is turning.