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

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!!!

set each factor equal to 0

4x-3 = 0

2x-1 = 0

solve for x.

4x-3=0

4x=3

x= 3/4

solve for x. 

2x-1= 0

2x= 1

x= 1/2

your answer should be 1/2 is less than or equal to x and 3/4 is greater than or equal to x

49/6 is going to equal 8 1/6