A hot air balloon rising vertically is tracked by an observer located 4 km from the lift‑off point. At a certain moment, the angle between the observer's line of sight and the horizontal is 𝜋5, and it is changing at a rate of 0.1 rad/min. How fast is the balloon rising at this moment?
Let 𝑦 be the height of the balloon (in km), 𝑡 be time (in minutes), and 𝜃 the angle between the line‑of‑sight and the horizontal (in radians).
(Use decimal notation. Give your answer to two decimal places.)
𝑑𝑦𝑑𝑡 =
y/4 = tanθ
1/4 dy/dt = sec^2θ dθ/dt
so plug and chug