A plane is heading due north and climbing at the rate of 60

A plane is heading due north and climbing at the rate of 60 km/hr If its airspeed is 460 khr and there is a wind blowing 90 km/hr to the northwest, what is the ground speed of the plane? ground speed Enter your answer as a NUMBER (not a vector), using exact values or at least 4 decimal place accuracy.

Solution

planes airspeed = 460km/hr

climbing at a rate = 60km/hr

applying pythagoras theorem to find the x component

460^2 = 60^2 + x^2

Vx = 456

Plane \'s Vector : V = 456i + 60k

Wind\'s vector is w = 90cos45i +90sin45j

=63.64i + 63.64j

Total velocity vector relative to the ground = 456i + 60k+ 63.64i + 63.64j

= 519.64i + 63.64j +60k

So velocity of plane relative to the ground = sqrt(519.64^2 +63.64^2 +60^2)

= 526.94 km/hr