A balloon is tied to a ground point by a cable that can extend and retract
MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A balloon is tied to a ground point by a cable that can extend and retract. At a particular instant the balloon is 42\,m horizontally from the tie-down point and 42\,m above it, so the cable makes an angle θ=4π with the ground. At that instant the balloon’s horizontal velocity is 4.0\,m\!/s away from the tie-down point and its vertical velocity is 2.0\,m\!/s upward. Compute dtdθ at that moment, expressing your answer in rad/s and indicating its sign.