An airplane departs from point a heading to an airport 520 km due north at point b. this plane flies at a speed of 240 km/h and a steady wind is blowing at 50 km/h toward the direction southeast. (a) in what proper heading (direction) should the plane head in order to fly north, from a to b, relative to ground?
(b) what is the speed of the plane relative to the ground?
(c) what is the time of flight from a to b? [(a) 8.5° west of north; (b) 202 kmh; (c) 2.57 hr.

a) 8.5° west of the north.

b) 202 kmh

c) 2.57 h

Explanation:

Let plane make x° angle west of north.

Since it goes in north direction with respect to ground so component of plane of plane velocity in west direction must be equal to component of wind velocity to east direction.

240sinx= 50sin45

Sinx= 0.147

x°= 8.5° west of the north.

b) velocity relative to the ground= 240Cos8.5°- 50cos45°

= 240×0.9890- 50/√2

= 202 kmh

c) the time of flight from A to B

time t= d/v

= 520/202= 2.57 h

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