Posted by Anonymous on Sunday, November 1, 2009 at 5:20pm.
Let
angle of elevation=θ
height of plane = H
horizontal distance from observer = x
tan(θ)=x/H
Use implicit differentiation
d(tan(θ))/dt = d(x/H)/dt
sec²(θ)dθ/dt = (dx/dt)/H
dθ/dt=(1/(Hsec²(θ))(dx/dt)
dθ/dt=(cos²(θ)/H)*(dx/dt)
Can you take it from here?
would you just replace H with 5 miles since that's the height the plane is flying at?
This is where you need to do some work.
The formula is general, but the numerical values you substitute have to be consistent in units.
For H=5 miles, and dx/dt=600 miles/hour, it would give dθ/dt in radians/hour.
You need to substitute values in appropriate units of your choice. Finally, you can also change radians to degrees using degrees=radians*180/π.
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