What bearing and airspeed are required for a plane to fly 700 miles due north in 3.5 hours if the wind is blowing from a direction of 338 degrees at 10 mph? The plane should fly at nothing mph at a bearing of nothing degrees. Calculator

1. Airspeed = 201.17 mph

2. Bearing  = 358.93⁰

Step-by-step explanation:

Given Data:

d = 700 mi

t = 3.5 hrs

speed of wind Vx = 10 mph

velocity of plane Vy = d/t

                                  = 700/3.5

                                  = 200 mph

1. Air speed (V) is calculated using the formula;

V² = V²x + V²y -2*Vx *Vy*cos∝

But ∝ = 338 - 180 = 158°

Substituting into the equation, we have

V² = 10² + 200² - 2*10*200*Cos 158

    = 40100 - 400 *(-0.92718)

    = 40100 + 370.872

 V²   = 40470.872

V = √40470.872

V = 201.17 mph

2. calculating the bearing using cosine rule, we have;

sin∅/Vx = sin∝/V

sin∅/10 = sin158/201.17

sin∅ = 10*sin 158/201.17

        = 3.746/201.17

       = 0.0186

∅ = sin⁻¹ 0.0186

   = 1.07

Therefore,

Bearing = 360 - 1.07

              = 358.93⁰

a

step-by-step explanation: