A balloon rises vertically at a constant rate of 4 m/s while an observer is 50 m from…

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

Problem

A balloon rises vertically at a constant rate of 4 m/s while an observer is 50 m from the launch point. If

\theta=\arctan\!\left(\dfrac{h}{50}\right)

, calculate

\dfrac{d\theta}{dt}

(in rad/s) when the balloon is 30 m above the ground. (a)

0.080

(b)

0.110

(c)

0.059

(d)

0.050