A hot-air balloon is observed from a point on the ground
MATHEMATICS · Subjective · AP · Calculus AB · Contextual Applications of Differentiation · Contextual Applications of Differentiation
Problem
A hot-air balloon is observed from a point on the ground. The balloon ascends vertically at 4.0 m/s while drifting horizontally away from the observer at 2.0 m/s. When the balloon is 30 m horizontally from the observer and 40 m above the ground, let θ be the angle (in radians) between the horizontal ground and the observer’s line of sight to the balloon. Compute dtdθ at that instant. State your answer in rad/s.