A hot-air balloon rises vertically at from a point on level ground

MATHEMATICS · Subjective · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

A hot-air balloon rises vertically at 4 m ⁣/ ⁣s4\text{ m}\!\big/\!\text{s} from a point on level ground. An observer stands 50 m50\text{ m} from that point. Determine the rate at which the observer’s angle of elevation θ\theta is changing when the balloon is 30 m30\text{ m} above the ground. Express your answer in radians per second.

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