Question

An airplane pilot sets a compass course due west and maintains an airspeed of 214 km/h . After flying for a time of 0.470 h , she finds herself over a town a distance 119 km west and a distance 13 km south of her starting point.

a. Find the magnitude of the wind velocity.

b. Find the direction of the wind velocity

c. If the wind velocity is 37 km/h due south, in what direction should the pilot set her course to travel due west? Use the same airspeed of 214 km/h .

Answer 1

a)

= velocity of airplane relative to wind = - 214 i + 0 j

t = time of travel = 0.470 h

= initial position = 0 i + 0 j

= Final position = - 119 i - 13 j

= Velocity of airplane relative to ground = ( - )/t = ((- 119 i - 13 j) - (0 i + 0 j))/0.470 = - 253.2 i - 26.66 j

= velocity of wind relative to ground

Using the equation

= -

- 214 i + 0 j = (- 253.2 i - 26.66 j) -

= - 39.2 i - 26.66 j

magnitude of the velocity is given as

|| = sqrt((- 39.2)² + (- 26.66)²)

|| = 47.4 km/h

b)

Direction : = tan^-1(- 26.66/(- 39.2)) = 34.22 deg South of West.