# Physics homework pretaining to Trigonometry.

• Sep 30th 2009, 01:29 PM
Caturdayz
Physics homework pretaining to Trigonometry.
"A car drives west for 150 KM. Then turns southwest and drives for 60 KM at an angle of 30 degrees. Finally the car drives 100 KM northeast at an angle of 60 degrees. What is the displacement?"

I think know how to set this problem up, but, I have a couple questions, and you guys have been a whole lot more helpful than my teacher.

Alright, for the first side I've got...

x1=150
y1= 0

and side 2... (The adjacent side, not the hypotenuse)

x2= Cos(30)*60
y2= Sin(30)*60

And the hypotenuse:

x3= Cos(60)*100
y3= Sin(60)*100

My main worry is that I've got my Sin and my Cos right.

Any help would be greatly appreciated.
• Sep 30th 2009, 02:19 PM
skeeter
Quote:

Originally Posted by Caturdayz
"A car drives west for 150 KM. Then turns southwest and drives for 60 KM at an angle of 30 degrees. Finally the car drives 100 KM northeast at an angle of 60 degrees. What is the displacement?"

note that east (+) , west (-) , south (-) , north (+)

$\displaystyle x_1 = -150$
$\displaystyle y_1 = 0$

$\displaystyle x_2 = -60\cos(30)$
$\displaystyle y_2 = -60\sin(30)$

$\displaystyle x_3 = 100\cos(45)$
$\displaystyle y_3 = 100\sin(45)$

$\displaystyle \Delta x = x_1 + x_2 + x_3$

$\displaystyle \Delta y = y_1 + y_2 + y_3$

$\displaystyle |\Delta r| = \sqrt{(\Delta x)^2 + (\Delta y)^2}$

$\displaystyle \theta = \arctan\left(\frac{\Delta y}{\Delta x}\right) + 180^{\circ}$