Question

An airplane flies due north with an air speed of260 km/h . A steady wind at 65 km/h blows eastward. (Air speed is the speed relative to the air.)

What is the plane’s ground speed (vpg)?

If the pilot wants to fly due north, what should his heading be?

Answer 1

In this the given the speed of the airplane relative to air is 260km/h duenorth

therefore v_pa = 260km/h due north

then v_pa,x = 0km/h

v_pa,y = 260km/h

also given speed of wind relative to ground is 65km/s dueeast.

therefore....the solution are....

v_ag = 65km/h due east

then v_ag,x = 65km/h

v_ag,y = 0km/h

Then

v_pg,x = v_pa,x +v_ag,x

Substitute the value.....

     = 0km/h + 65km/h

     = 65km/h

And v_pg,y = v_pa,y +v_ag,y

   =260km/h + 0km/h

     = 260km/h

Then

v_pa = sqrt[(65km/h)² +(260km/h)²]

   =268km/h

direction is tan^-1(260/65) = 75.9^otoward north of east