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

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)((52)/(280)* (1)/(√(2)))`

`x = 7.547^(\circ)` south- west