Question

A balloon is rising vertically over a point A on the ground at the rate of 15 ft./sec. A point B on the ground is level with and 30 feet from A. When the balloon is 40 feet from A, at what rate is its distance from B changing?

Answer 1

Step-by-step explanation:

Let r be the distance between the ballon and point B. Let v be the vertical distance the balloon is over point A.

r²=40²+30²

r↓3=2500

r=50

r²=v²+900

2r*dr/dt=2v*dv/dt Then substitute r=50; v=40; and dv/dt=15m/s:

2*50*dr/dt=2*40*154m/s

100dr/dt=1200m/s

dr/dt=12m/s

At that point in time the balloon is moving away from point B at a rate of 12 meters per second.

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Answer 2

your answer is 12m/s .

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