Polar Coordinate Tracking problem

[AirForceOne]

Homework Statement

You're tracking a plane from the ground. The plane is at a constant height h from the ground, at a distance r from you at the illustrated instant, and at an inclination theta. The plane's speed is constant at 1200km/hr. Find the rate at which your tracking dish must rotate if r=3km and theta=30degrees. Does the acceleration of gravity make any contribution to your answer?

The attempt at a solution

The correct answer is 0.05 rad/s.

But this is what I got:

Sorry for the gigantic image!

Thanks.

 

[vela]

Check your units.

 

[AirForceOne]

461.88 rad/hr = 0.1283 rad/s

Thanks for pointing that out. Still wrong though :/

 

[vela]

You resolved i into e_r and e_θ incorrectly. (Try it with θ=90 degrees, for example.) Also, the r in your expression for V isn't equal to 3 km.

 

[AirForceOne]

Why isn't it 3km?

 

[vela]

I guess it depends on how you interpret the phrase "distance from you." But if you use r=3000 m, the answer is 0.056 rad/s, which rounds to 0.06 rad/s. If you use 3000 km as the horizontal distance from you, you get 0.048 rad/s, which rounds to the answer you cited.

 

[AirForceOne]

Thank you very much. I got 0.06.

What is the meaning of the second part of the question ("Does the acceleration of gravity make any contribution")?

Thanks again.

 

[vela]

Would you get a different answer if, say, you were on Mars, where the acceleration of gravity is different?