An airplane pilot wishes to fly due west. A wind of 82.0m/s is blowing toward the south.If the airspeed of the plane (its speed in still air) is 375.0 km/h, in which direction should the pilot head? What is the speed of the plane over the ground?

Answer 1

wind speed + plane speed= speed over ground

82S+375@direction=speed W

so,
375@direction= W-82S=W+82N

375SinTheta N+ 375CosThetw W is what you want.

82=375 sinTheta solve for Theta.
That is the direction N of W.
Speed over ground? 375CosTheta.

Answer 2

first convert km/h to m/s then squre both the numbers and then add them. after this you will have one big number. you then get the square root of this number and that is the speed of the plane over the ground