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Classical Mechanics

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Moderate

Expression for Ground Speed

CLMECH-YW0PNE

Aircraft can directly measure their airspeed, $\vec{a}$, which is the velocity measured relative to static air. To get the velocity relative to a stationary point on the ground (i.e. ground speed), you need to add the airspeed of the plane to the speed of the air itself (i.e. the wind velocity, $\vec{w}$).

Consider an aircraft flying straight north with wind blowing at an angle $\theta$ as shown below.

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What is the expression for the northward component of the ground velocity?

A

$|\vec{a}|\sin\theta$

B

$|\vec{a}| + |\vec{w}|\cos\theta$

C

$|\vec{a}| + |\vec{w}|\sin\theta$

D

$|\vec{a}|\sin\theta + |\vec{w}|\cos\theta$

E

$|\vec{a}|\cos\theta + |\vec{w}|\sin\theta$