Mathematics

Mathematics

Problem

A hot-air balloon rises vertically so that its height hh (in meters) and the observer’s angle of elevation θ\theta (in radians) satisfy tan⁡θ=h120\tan\theta = \dfrac{h}{120}. When θ=0.5\theta = 0.5 rad, the angle is increasing at a rate of 0.030.03 rad/s. Determine dhdt\dfrac{dh}{dt} at that instant, including proper units.

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