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makvit
1 month ago
15

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]1 month ago
6 0

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.

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