Vector Word Problem

**HawthorneKitty** · April 19th 2009, 06:49 PM

Problem:
An airplane travels north with an airspeed of 300 mph. There is a wind from the southwest at 50 mph. What is the resulting course of the plane. (magnitude and direction)

I'm not sure, but does magnitude refer to speed it is traveling at, and I'm not sure how one calculates direction, but is that the angle at which it travels from its initial point?

Hopefully somebody can help me; and thank you for reading.

**skeeter** · April 19th 2009, 07:18 PM

Originally Posted by HawthorneKitty

Problem:
An airplane travels north with an airspeed of 300 mph. There is a wind from the southwest at 50 mph. What is the resulting course of the plane. (magnitude and direction)

air vector + wind vector = ground vector

$A_x + W_x = G_x$

$0 + 50\cos(45) = G_x$

$A_y + W_y = G_y$

$300 + 50\sin(45) = G_y$

$|G| = \sqrt{G_x^2 + G_y^2}$

direction relative to the +x-axis (East) ...

$\theta = \arctan\left(\frac{G_y}{G_x}\right)$

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