Question

A plane is heading due north and climbing at the rate of 100 km/hr. If its airspeed is 470 km/hr and there is a wind blowing 120 km/hr to the northwest, what is the ground speed of the plane?

Answer 1

Let's use vector notation for solving this problem.

Also, ground speed of plane = airspeed of plane + wind-blowing speed. ..,........... (1)

Let's say unit-vector along west and north direction are i and j respectively.

Then unit cell vector along northwest = (i+j)/√2

Now, airspeed of the plane = (470 kph) j

And, wind blowing speed = (120 kph)*(i+j)/√2

Using formula(1),

Ground speed of plane =  (470 kph)j + (120 kph)*(i+j)/√2

= (84.8528137)i + (554.852814)j kph

So magnitude of ground speed of plane = 561.303521 kph,

Direction from West to North side , = arctan( 554.852814/84.8528137) = 81.30520631° .