A Ballons rises at the rate of 8 ft/sec from a point on the ground 60 ft from the observer. Find the rate of change of the angle of elevation when the balloon is 25 ft above the ground.
Let a= 60 ft
Let b= 25 ft
Let db/dt= 8
Find d(theta)/dt
Formula relating angle of elevation to height of balloon and distance from observer.
tan(theta)=b/60
Differentiate implicitly, and solve for d(theta)/dt:
d(theta)/dt = (cos^2(theta)/60) * (db/dt)
Need to find what theta is when balloon is 25 ft above ground:
USE:
arctan(5/12)= theta
Now plug theta and db/dt into the equation and I got:
d(theta)/dt= 1152/169 radians/second
Something doesn't seem right, I either missed up on a step, am paranoid, or both.
2007-10-14
10:15:02
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2 answers
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asked by
Dr. AjC ♍
3