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Anaeroplane fliesalonga straightpathA to Bandbackagainthedistancesbetweena and Bis1 andthe aeroplanemaintainsthe constantspeedv . There issteadywindwith aspeedu atan anglethetawithlineAB . determinetheexpression forthe totaltimeofthetrip . |
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Answer» Solution :VELOCITYOF planealongAB= Vcos ` ALPHA- u costheta` andfor no- driftfromline ` AB: vsin alpha= u sintheta impliessin alpha= ( u sin theta)/( v)` timetakenfromA to B`t_(AB )= (t )/(v cosalpha- UCOS theta)` B to A velocityofplanealongBA ` = v cosalpha+ u costheta ` andfor nodriftfromlineAB`: v sinalpha= usin thetaimpliessin alpha= (u sin theta)/( v)` timetakenfromBtoA: ` v sinalpha= u sinthetaimpliessinalpha=( u sin theta )/( v) ` timetakenfromB to `A: t_(BA)= ( t)/(v cosalpha+ u costheta)` totaltimeteken ` = T_(AB ) +t_(BA) = ( 2v lcosalpha)/( v^2cos ^2alpha- u^2cos ^2theta )= ( 2 vt sqrt((u^2 sin ^2 theta))/(v^2))/(v^2 -u^2 )` 
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