A hot air balloon rising vertically is tracked by an observer located 4 miles from the life off point. At a certain moment, the angles between the observers line of sight and the horizontal is Pi/4 and it is changing at a rate of 0.1. How fast is the balloon rising at this moment

Answer 1

At height h,

h/4 = tanθ
1/4 dh/dt = sec^2θ dθ/dt
So, plug in your numbers and find dh/dt