a hot air balloon rising vertically is tracked by an observer located 2 miles from the lift-off point. at a certain moment, the angle between the observer's line-of-sight and horizontal is pi/5

Question

a hot air balloon rising vertically is tracked by an observer located 2 miles from the lift-off point. at a certain moment, the angle between the observer's line-of-sight and horizontal is pi/5, and it is changing at a rate of 0.1 rad/min. how fast is the balloon rising at this moment?

Answer 1

Bob, the key to these related rate problems is to draw a sketch and then:

1) Find the rates which are related (here the rates which are related to each other, but not equal, are the rate the balloon rises and the rate the angle of observation increases)

2) Find the permanent relation, then take the derivative to get the rates (here it is tan(theta)) = h/2)

Now you can take the derivative of both tan(theta) and h/2 (make sure to apply the chain rule so you have d(theta)/dt on one side and dh/dt on the other) and insert the given information.

Hope this helps, but please let me know--Andrew