Question

An airplane flies at airspeed (relative to the air) of 280 km/h . The pilot wishes to fly due North (relative to the ground) but there is a 52 km/h wind blowing Southwest (direction sehgal (ts35972) – Homework 3 – markert – (54390) 4 225◦ ). In what direction should the pilot head the plane (measured clockwise from North)?

Answer 1

Answer:

the pilot should head the plane $7.547^{\circ}$ towarrds south- west

Solution:

The airspeed of the airplane, v = 280 km/h

The velocity of the wind, v' = 52 km/h South-west

Angle, $\theta = 225^{\circ}$

Now, measured angle in the clockwise direction from North:

$sin225 = sin(\pi + 45) = - sin 45^{\circ}$

Now,

$vsinx - v'sin45 = 0$

$280sinx = 52sin45$

$x = sin^{- 1}(\frac{52}{280}\times \frac{1}{\sqrt{2}})$

$x = 7.547^{\circ}$ south- west