A hot air balloon rising straight up from a level field is tracked by a range finder 500 ft from the lift-off point. At the moment the range finder's elevation angle is `(pi)/(4)`. The angle is increasing at the rate of `0.14 ` rad/min. How fast is the balloon rising at the moment ?

Explanation

`y=500 tan theta`
` rArr" " (dy)/(dt)=500 (d tan theta)/(dt) =500 (d tan theta)/(d theta) (d theta)/(dt)`
`=500 sec^(2) theta (d theta)/(dt)`
`=500 xx 2 xx 0.14`
`= 140 ft//"min"`