Respuesta :
Answer:
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
The airspeed is 201.17 mph and bearing is [tex]358.93^\circ[/tex] and this can be determined by using the vector form of velocity.
Given :
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.
To determine the airspeed the following formula can be used.
[tex]\rm V^2 = V^2_x +V^2_y-2V_xV_y cos \theta[/tex] ---- (1)
where, [tex]\theta = 338-180 = 158^\circ[/tex], [tex]\rm V_y[/tex] is the velocity of the plane and [tex]\rm V_x[/tex] is the velocity of the wind.
Now, put the value of [tex]\rm V_y[/tex], [tex]\rm V_x[/tex] and [tex]\theta[/tex] in the equation (1).
[tex]\rm V^2 = 10^2+200^2+2\times 10\times 200\times cos158[/tex]
[tex]\rm V^2= 100 + 40000+4000(-0.9271)[/tex]
V = 201.17 mph
Now, using cosine rule:
[tex]\rm \dfrac{sin \alpha}{V_x}=\dfrac{sin \theta }{V}[/tex]
[tex]\rm \dfrac{sin\alpha }{10}=\dfrac{sin158}{201.17}[/tex]
[tex]\rm sin\alpha =10\times \dfrac{sin158}{201.17}[/tex]
[tex]\rm sin \alpha = \dfrac{3.746}{201.17}[/tex]
[tex]\rm sin\alpha =0.0186[/tex]
[tex]\alpha = 1.07^\circ[/tex]
Therefore, the bearing is given by 360 - 13.07 = [tex]358.93^\circ[/tex]
For more information, refer to the link given below:
https://brainly.com/question/24376522
