A hot air balloon rising vertically is tracked by an observer located 4 miles from the lift-off point.

Question

A hot air balloon rising vertically is tracked by an observer located 4 miles from the lift-off point. At a certain moment, the angle between the observer's line-of-sight and the horizontal is π/3 , and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this moment?

_____ miles/min?

Answer 1

It always helps to draw a triangle to demonstrate what's going on. Usually you'd use pythagorean theorem as the equation unless information about the angle is given as in this case. Choose a trig function based on which sides are given or relevant so that is tan in this case because opp and adj are relevant. Derive the equation and plug in given values. Then you can solve for the rate that is needed.