confusing physicis problem! HELP!?

Question

i think if you know how to do it...itsprobaly not hard..but my teacher did one problem that was nothing like this so i have no idea what to do! Heres the problem:
A car is driven 125 km W and then 65 km southwest. What is the displacement of the car from the point of origin (magnitude and direction)? Draw a diagram...i think its using the vectors things...help please! I have hw on this stuff and i have no idea where to start

Answer 1

First you need these general equations:
Magnitude "r" = Sqrt ( (sum Y)^2 + (sum X)^2)
Direction : Tan(angle) = Y/X

First Draw the diagram.
Start at origin. Draw 125 Units to the left. From there Draw 65 units at an 45 degree angle. Now Draw one more line that connects that end to the origin. Now you have a Triangle. You can solve this using either Law of cosines or Vectors addition.

Solution:
Let's use Vector addition. First Sum up all of the forces in the Y direction which is:
Sum(Y) = -125 -65Cos45
now do the X direction:
Sum(X) = -65Sin45

Now just plug it into the above equations:
Magnitude = Sqrt[ (-125-65Cos45)^2 + (-65Sin45)^2]
That should give you Approximately 177.03Km

Now for Direction:
Solve first for angle so that "angle" = InverseTan (y/x)
Plug that in and you should get approx: -15.05 degrees or add 180 to get -165.05 degrees

That's all you need for this problem. I might have made a small math error somewhere since I didn't check the work and was doing it really quick but it should be correct.

Answer 2

Here's the image
http://i142.photobucket.com/albums/r88/odu83/cardrive.jpg


I used North and East as positive.
The car went 125 km due West, which is negative on the horizontal axis.
The car then went SW 65 km, which is at a 45 degree angle down and to the left, so the horizontal is
-125-65*cos(45)
and the vertical is
-65*sin(45)
the car ends up at the point
-176, -46
the displacement is
sqrt(176^2+46^2)

j

Answer 3

Draw an arrow with length 125 mm at 270 deg, from the end of the arrow draw another arrow with length 65 mm at 245 deg (you draw the problem with scale 1mm = 1 Km), that is all the new place you are in is the end of the second arrow. the length you go west is 125 + 65 cos45 = 125 + 45.96 = 170.96Km, and you go south 65 sin45 = 45.96 Km