Respuesta :
Answer:
The speed of the plane relative to the ground is 300.79 km/h.
Explanation:
Given that,
Speed of wind = 75.0 km/hr
Speed of plane relative to the air = 310 km/hr
Suppose, determine the speed of the plane relative to the ground
We need to calculate the angle
Using formula of angle
[tex]\sin\theta=\dfrac{v'}{v}[/tex]
Where, v'=speed of wind
v= speed of plane
Put the value into the formula
[tex]\sin\theta=\dfrac{75}{310}[/tex]
[tex]\theta=\sin^{-1}(\dfrac{75}{310})[/tex]
[tex]\theta=14.0^{\circ}[/tex]
We need to calculate the resultant speed
Using formula of resultant speed
[tex]\cos\theta=\dfrac{v''}{v}[/tex]
Put the value into the formula
[tex]\cos14=\dfrac{v''}{310}[/tex]
[tex]v''=\cos14\times310[/tex]
[tex]v''=300.79\ km/h[/tex]
Hence, The speed of the plane relative to the ground is 300.79 km/h.
The speed of the plane relative to the ground is 300.7 km/h.
The pilot should head to the ground.
Speed
Given that speed of wind is 75.0 km/hour and the airspeed of the plane is 310 km/hour.
The angle between the direction of the plane and wind is calculated as given below.
[tex]sin \theta = \dfrac {v_w}{v_p}[/tex]
Where v_w is the speed of wind and v_p is the speed of the plane.
[tex]sin \theta = \dfrac {75}{310}[/tex]
[tex]sin \theta = 0.24[/tex]
[tex]\theta = sin^{-1} 0.24[/tex]
[tex]\theta = 14^\circ[/tex]
The angle between the direction of wind and plane is 14 degrees.
The relative speed of the plane is calculated as given below.
[tex]cos \theta = \dfrac {v}{v_p}[/tex]
Where v is the relative speed of the plane.
[tex]cos 14^\circ = \dfrac {v}{310}[/tex]
[tex]0.97 \times 310 = v[/tex]
[tex]v = 300.7 \;\rm km/hr[/tex]
Hence we can conclude that the speed of the plane relative to the ground is 300.7 km/h.
To know more about the speed, follow the link given below.
https://brainly.com/question/7359669.
