An airplane pilot wishes to fly directly westward. According to the weather bureau, a wind of 75.0 km/hour is blowing southward.

Question

3 months ago

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An airplane pilot wishes to fly directly westward. According to the weather bureau, a wind of 75.0 km/hour is blowing southward.

The speed of the plane relative to the air (called the air speed) as measured by instruments aboard the plane is 310 km/hour . In which direction should the pilot head?

Physics

1 answer:

Softa [3K] · Answer 1 · 2026-02-26T06:25:39+03:00

Answer:

The plane's speed in relation to the ground is 300.79 km/h.

Explanation:

Provided details include:

Wind speed = 75.0 km/hr

Plane's airspeed = 310 km/hr

Next, we must find the ground speed of the plane

Calculating the angle

Using the angle formula

$\sin\theta=\dfrac{v'}{v}$

Where v' represents the wind speed

v represents the plane's speed

We will substitute the values into the formula

$\sin\theta=\dfrac{75}{310}$

$\theta=\sin^{-1}(\dfrac{75}{310})$

$\theta=14.0^{\circ}$

Now, we must find the resultant speed

Using the resultant speed formula

$\cos\theta=\dfrac{v''}{v}$

Insert the values into the formula

$\cos14=\dfrac{v''}{310}$

$v''=\cos14\times310$

$v''=300.79\ km/h$

Consequently, the plane's speed in relation to the ground equals 300.79 km/h.