Vectors and Airplane Direction

[disneychannel]

Homework Statement

An airplane is heading southwest at 600 mph and encounters a wind blowing from the west.

a)calculate the planes destination of the wind is blowing 30 mph.
b)calculate the planes destination if the wind is blowing 90 mph.



2. The attempt at a solution

a) <30cos0, 30 sin0>
<600cos225, 600sin225>
<30cos0+600cos225, 30sin0+600sin225>
30sin0+600sin225=-424.26
360+424.264=784.26 bearing direction

i don't know if this is right or how to do it! HELP
b) same as above but except 30 put 90

 

[nate808]

Hello!

To calculate the plane's destination, we can use vector addition. This means we need to add the velocity of the plane to the velocity of the wind. The direction of the wind is given as "from the west", so we can represent it as <30,0>, since it is only affecting the plane's x-axis motion.

a) If the wind is blowing at 30 mph, the resulting destination would be:

<600,0> + <30,0> = <630,0>

This means the plane's destination would be 630 miles southwest.

b) If the wind is blowing at 90 mph, the resulting destination would be:

<600,0> + <90,0> = <690,0>

This means the plane's destination would be 690 miles southwest.

I hope this helps! Let me know if you have any further questions.