Question

An airplane with a speed of 120 knots is headed west while a 30-knot wind is blowing from 120°. Find the ground speed to the nearest knot. 131 knots 141 knots

Answer 1

Answer:

Velocity of the plane relative to the ground

= [(-145.98î) + (15j)] knots

Magnitude = groundspeed = 146.75 knots

Direction = -5.9°

Step-by-step explanation:

This is a relative velocity question.

Let the velocity of the airplane relative to the wind be V(aw)

Velocity of the airplane relative to the ground = Va

The velocity of the wind relative to the ground = Vw

The relative velocity theory enables us o relate these as thus,

V(aw) = Va - Vw

Va = V(aw) + Vw

V(aw) = (-120î) knots (120 west)

For Vw, the wind is said to be blowing from 120°, reading this on a three figure bearing as angle from the north,

This gives the real direction of the wind to be 150° from the positive x-axis as shown in the attached image.

Vw = (30cos 150°)î + (30sin 150°)j

Vw = (-25.98î + 15j) knots

Va = V(aw) + Vw = (-120î) + (-25.98î + 15j)

Va = (-145.98î) + (15j)

Magnitude of Va = √[(-145.98)² + (15)²] = 146.75 knots

Direction = tan⁻¹ (-15/145.98) = -5.9°

Hope this Helps!!!