# Angular Velocity

1. Jun 29, 2009

### Tsizzle

1. The problem statement, all variables and given/known data
A revolving light which 50sqrtroot3 away from the shore, revolves in a constant angular velocity, the spot of the light moves along the straight shore at a rate of 300m/s when it is 50 m from the point on the shore which is closest to the light. Find the Angular velocity.

3. The attempt at a solution
I am confused by this question. If the angular velocity is Constant, and the velocity given is 300m/s isnt the answer also 300 m/s?

it says the revolivng light is 50sqrtroot 3 m away which is 86 meters.
so i am guessing the hypotenuse is 86 m. and the length of the other side is 50 m. therefore
a= sqrtroot(b^2 - c^2)
so the final side must be 70 m ?

where do i go from there?

Thank you for looking, I really appreciate it!

2. Jun 29, 2009

### Staff: Mentor

The rate at which the light moves along the shore is not constant, and is 300 m/s only at the given point. At the point on shore that is closest to the light, the linear velocity will be the smallest. The farther away from this point, in either direction, the higher the linear velocity. If the shoreline happened to be circular and the light were at the center of the circle, the problem would be trivial.

You are supposed to calculate the angular velocity of the light from the linear velocity and the distance from the shore. This seems to me to be a related rates problem, so you want to get a relationship between a section of the shore (one side of a triangle) and the angle at the light, and from this equation get an equation that relates the derivatives dy/dt and dtheta/dt.

Also, 50 sqrt(3) is closer to 87 than 86. Don't convert radicals to their approximate values until your final step, otherwise you will get a result that is off.