An airplane can travel through still air at 810 km/h. The pilot points the airpl

Question

An airplane can travel through still air at 810 km/h. The pilot points the airplane due north. As soon as he takesoff, a wind blowing to the west at 65 km/h is encountered and blows the airplane off-course and the windcontinues throughout the flight. a.What is the plane’s velocity relative to the ground? b.If the plane flies over a boat which is traveling north in a still lake at 10 km/h, what is the plane’s velocityrelative to the boat? c.If the plane flies for 2.5 hours, what is its position (magnitude and direction) from the starting point?

Explanation / Answer

let unit vector in direction of north is j and in east direction is i and in west is -i and in soth it is -j

we assume all in X and Y plane

vp=810j ; vair =-65i

So vplane relative to eart =810j-65i

part b

vboat/earth=10j

so Vplane/boat=810j-65i-10j=800j-65i

part c

position of plane in 2.5 hour=v*t=2.5(810j-65i)=2025j-162.5i

magnitude=(20252+162.52)1/2=2031.509m from origin point

direction=tan-1(2031.509/162.5) =85.42 degree west to north

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