An Observer Watches A Hot Air Balloon Rise 100m Fr

LondonMath6

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An observer watches a hot air balloon rise 100m from its liftoff point. At the moment the angle is pi/6, the angle is increasing at the rate of 0.1 rad/min. How fast is the balloon rising at that moment?

 

Answer No.1

Anonymous

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Tanθ= H/b ( where H = height , b = base{ constant}) tan(π/6 )= 100/b b= 100/√3 differeenatting both sides wrt time, we get sec2θ ( dθ/dt) =(1/b) (dH/dt) sec2( π/6) ( 0.1) = 100/√3( dH/dt) (0.4/3)(√3/100) = dH/dt dH/dt = 0.0023 m /min apprx

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