Simple vectors?!?! i can't figure it out?

Question

A car drives 200km west and then 80km southwest...what's the magnitude and dir? whoever shows instead of just answer gets best answer ^_^

Answer 1

200Km vector: 180 degrees with the +x-axis

80Km vector: 225 degrees with the +x-axis: 45 (southwest) + 180

sum the x components:

sumX = 200*Cos(180) + 80 * Cos(225) = -256.68Km

Note: 200*Cos(180)=-200

sum the y components:

sumY = 80*Sin(180) + 80 * Sin(225)= -56.56Km

Note:  80*Sin(180) =0

resultant vector magnitude: sqr(sumX^2+sumY^2) = 262.73Km

direction: Angle with the positive x-axis:

atan(sumY/sumX)= 192.43 degrees

Answer 2

the answer is 20.784 km from12.44 (deg.) east

Answer 3

ok, what you do is make a triangle out of it. One leg will be your car going 200km west, the second will be it going 80km SW. The third leg, just draw it in, is the new vector, the sum of the two other vectors. Now just use law of sines, or law of cosines, whichever you prefer, to figure out the angle and value you are looking for.

Answer 4

to start it is

200cos 180

80cos225

-256.56

200sin 180

80 cos 225

-56.56

-tan inverse(56.56/256.56)= 12.43 +180

256.56^2+56.56^2=262.7(this number was square rooted

so 262.7@192.43

Answer 5

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