# Needing help with a vector word problem

• May 13th 2009, 08:36 PM
Shanizzle
Needing help with a vector word problem
I'm taking my word problem final in two days and I really need to understand this ASAP. Here' s the problem:

A place is flying on a bearing of South 10 degrees East at 460 mph. A tail wind is blowing in the direction of South 20 degrees West at 80 mph. Find the resultant velocity of the plane and give a graphic representation of the resultant vector.

I'm just having problems finding angles and understanding so that I can use the Law of Cos.

Thank you.
• May 13th 2009, 09:01 PM
TheEmptySet
Quote:

Originally Posted by Shanizzle
I'm taking my word problem final in two days and I really need to understand this ASAP. Here' s the problem:

A place is flying on a bearing of South 10 degrees East at 460 mph. A tail wind is blowing in the direction of South 20 degrees West at 80 mph. Find the resultant velocity of the plane and give a graphic representation of the resultant vector.

I'm just having problems finding angles and understanding so that I can use the Law of Cos.

Thank you.

Here is a diagram

Attachment 11410

$\displaystyle V_1=(460\cos(350),460\sin(350))$

$\displaystyle V_2=(80\cos(200),80\sin(200))$

$\displaystyle V_1+V_2 \approx (377.8,-107.2)$

So the resultant velocity is the magnitute of the sum of the vectors or

$\displaystyle ||V|| \approx \sqrt{(377.8)^2+(-107.2)^2}$