Question

The pilot of a light plane heads due North at an airspeed of 240 km/h. A wind is blowing 90 km/h at an angle of 30 degrees E of N relative to the ground.

A) What is the plane’s velocity with respect to the ground (give both magnitude and direction) if the pilot does not correct her course?

B) In order to fly north (relative to the ground) , the pilot must fly into the wind at some angle. If she maintains her airspeed what angle must she fly into the wind and what will be her new ground speed?

Answer 1

A] velocity of plane wrt ground = velocity of plane in air + wind velocity

= 240 North + 90*cos 30 degree North + 90 sin 30 degree East

= 317.9 km/h North + 45 km/h East

= sqrt(317.9^2+45^2)

= 321 km/h at angle arctan(45/317.9)

= 321 km/h at 8.056 degree East of north

B] Let the angle be A,

West component of plane's velocity = East component of Wind velocity

240*sin A = 90*sin 30 degree

240 sin A = 45

A = arcsin(45/240)

= 10.8 degree West of north answer