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**Menudo** A hot air balloon is rising straight up from a level field and is tracked by a range finder 500ft from the lift point. At the moment the range finder's elevation angle is pi/4, the angle is increasing by .14 radians per minute. How fast is the balloon rising at that instant.

Why do you doubt yourself?

Code:

.
/|
/ |
/ |
/ h
/ |
/ |
/ θ |
--o-------500----+

As you observed, we have

So, we differentiate implicitly with respect to time ,

When the angle is , we have , so we substitute:

If you carry through the units, you should see that we have feet per minute, so the balloon is rising at a rate of .