Luke W.

asked • 01/10/18

I need help checking a related rates problem I made. Please help!

As part of a project, I need to create a related rates problem. I made one, but when I work it out, I get an answer that doesn’t look right. This is the problem: A bird is flying north at a speed of 70 ft/sec, 100 ft above the ground. At a certain moment, an observer directly north of the bird is 125 ft from it. At this moment, if the observer is watching the bird at an angle from the ground of 30 degrees, then what is the rate at which the angle is changing? There is my problem, and I would appreciate knowing what you get as your answer.

Doug C.

Another way to think about it:
At the instant the bird starts flying (or the observer starts watching) the angle is close to 39 degrees (arc tan (100/125)). As the bird keeps flying and the observer keeps watching this angle is increasing, so will only become 30 degrees as the bird flies directly overhead and then starts flying away from the observer. It is unlikely that is what you intended. Instead ask the question how fast is the angle changing when the angle of elevation is 45 degrees (for example).
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01/10/18

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Edward A. answered • 01/10/18

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Your first challenge may be that the angle is not 30 degrees. 
Since the bird is flying at 100', and the observer is 125' distant (I assume you mean ground distance, rather than a 125' hypotenuse), sin(theta) is .6246, but sin(30) is .5.

So perhaps your calculation is thrown off by that discrepancy. Try again.
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