Arock is dropped straight off a bridge that is 9 meters above the ground and falls at a constant speed of 10 m/sec. another person is 12 meters away on the same bridge. at what rate is the distance between the rock and the second person increasing just as the rock hits the ground?

6m/s

Explanation:

We are given that height of rock from the ground=9 m

Constant speed=10 m/s

Distance of person from rock=12 m

We have to find the rate at which distance between the rock and the second person increasing just as the rock hits the ground.

In triangle ABC

Let AB=x, BC=y,AC=z

(using pythagorous theorem )

Differentiate w.r.t

Hence, the rate at which distance between rock and person increasing just as the rock hits the ground=6 m/s

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