Question

The speed of an aircraft in still air is 300 km/h. The wind velocity is 60 km/h from
the east. The aircraft is steered on the course in the direction 60°
. Find the true
velocity of the aircraft.

Answer 1

The true velocity is 250 km/h.

Explanation:

As the aircraft is moving with speed of 300 km/h and the wind velocity is in east direction with the magnitude of 60 km/h. The resultant velocity or the true velocity can be found by the vector addition of the velocities.

If the true velocity is represented as V and the velocity of aircraft is represented as vₐ and the velocity of wind as vₓ, then

V² = vₐ² + vₓ² - vₐ.vₓ cosθ

So, the angle formed between them is 30°

Then, V² = (300)² + (60)² - 2×(300×60) cos 30°

V²=90000+3600-31177=62423

V =250 km/h

So, the true velocity is having magnitude of 250 km/h.

Thus, the true velocity is 250 km/h.