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A balloon is rising vertically from a le...

A balloon is rising vertically from a level field , suppose an on-looker sees it rising at 0.14 rad/min. when `theta=(pi)/(4)` (when the on -looker is 500 m away from the launch spot ), how fast is balloon rising ?

Text Solution

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Given , `(d theta)/(dt)=0.4`
In given figure ,
`tan theta=(y)/(500)`
Differentiate with respect to t
`sec^(2) theta ""(d theta)/(dt)=(1)/(500)(dy)/(dt)`
`((dy)/(dt))_(theta=(pi)/(4))=500xx2xx0.14=140` m/min.
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