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A light plane is headed due south with a speed of 185 km/h relative to still air. After 1.00 h, the pilot notices that they have covered only 135 km, and their direction is not south but15.0oeast of south. What is the wind velocity?

Short Answer

Expert verified

The velocity of the wind is 64.82kmhat 32.62°east of north.

Step by step solution

01

Step 1. Given data

The resultant velocity of the light plane is the vector sum of the aircraft's velocity relative to the wind and speed of the wind.

Given data:

The speed of the plane relative to still air is vpa=185kmh.

The time for the flight is t=1.00h.

The traveled distance is d=135km.

Assumptions:

Let vwgbe the wind velocity relative to the ground θoeast of north, andvpg be the plane's velocity relative to the ground.

02

Step 2. Calculation of the wind velocity and direction

Now, if the plane moves 135 km in 1.00 h, the plane's velocity relative to the ground is vpg=135kmh.

From the diagram,

vpg=vpa+vwgvwg=vpg-vpa

Then,

vwg=vpg2+vpa2-2vpgvpacos15°=135kmh2+185kmh2-2×135kmh×185kmhcos15°=64.82kmh

Now, using the sine formula,

vwgsin15°=vpgsinθsinθ=vpgvwg×sin15°θ=sin-1135kmh64.82kmh×sin15°θ=32.62°

Hence, the velocity of the wind is 64.82kmhat 32.62°east or north.

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