Solving Airplane Pilot Problem - Find Angle & Speed Over Ground

[clair_a_net]

oh I am having a problem trying to solve the following problem.

An airplane pilot wishes to fly due west. A wind of 88.0 is blowing toward the south.

with :If the airspeed of the plane (its speed in still air) is 375 , in which direction should the pilot head?

can't figure out how to solve for the angle. any pointers?


and to find the :What is the speed of the plane over the ground?


this part should be easier once i have the angle. i think

thanks
clair_a_net

 

[PhysicsDude55]

Think of it like a triangle.

Since the pilot wishes to fly due west, it must counteract the south wind with the Y component of the plane's velocity due north of equal magnitude. So one leg of the triangle is 88 mph north, or posotive Y if its easier to think that way.

The hypotenuse(sp?) must be 375 because that's how fast the plane is going, and the bottom leg of the triangle is the speed as it appears to be moving due west, or the X component of the velocity.

Using the pathagreon(sp?) theorum and some trig, the numbers should pop out no problem.