A small balloon is released at a point 150 feet away from an observer, who is on level ground. If the balloon goes straight up at a rate of 7 feet per second, how fast is the distance from the observer to the balloon increasing when the balloon is 14 feet high

Explanation:

Given that

x= 150 ft

y= 14 ft

From the diagram

When ,x= 150 ft and y= 14 ft

z=150.74 ft

By differentiating with respect to time t

Here x is constant that is why

Now by putting the values in the above equation we get

Therefore the distance between balloon and observer increasing with 0.65 ft/s.

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