A rocket ascends vertically at 3 m/s while an observer walks directly away from the…

MATHEMATICS · Single correct · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation

Problem

A rocket ascends vertically at 3 m/s while an observer walks directly away from the launch pad at 2 m/s. When the observer is 40 m from the pad and the rocket is 60 m above the ground, the angle of elevation satisfies θ=arctan⁡ ⁣(hx)\theta = \arctan\!\left(\dfrac{h}{x}\right), where xx is the observer’s horizontal distance from the pad. What is dθdt\dfrac{d\theta}{dt} at that instant? (a) 0.023 rad/s0.023\,\text{rad/s} (b) −0.010 rad/s-0.010\,\text{rad/s} (c) 0 rad/s0\,\text{rad/s} (d) 0.046 rad/s0.046\,\text{rad/s}

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