SOLUTION: After driving 30.0 km west, a car turns southwest and proceeds another 60.0 km. What is the displacement (in kilometers) of the car from the point of origin (magnitude only)?

Algebra ->  Vectors -> SOLUTION: After driving 30.0 km west, a car turns southwest and proceeds another 60.0 km. What is the displacement (in kilometers) of the car from the point of origin (magnitude only)?       Log On


   



Question 1189852: After driving 30.0 km west, a car turns southwest and proceeds another 60.0 km. What is the displacement (in
kilometers) of the car from the point of origin (magnitude only)?
I tried to do x=60sin45 so x=51.054 and y=30%2B60cos45 so y=61.519 then to find the magnitude of displacement I used MagofDis= sqrt%28x%5E2%2By%5E2%29
The answer I got was 6391.137567km but it does not look right.

Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52809) About Me  (Show Source):
You can put this solution on YOUR website!
.
After driving 30.0 km west, a car turns southwest and proceeds another 60.0 km. What is the displacement (in
kilometers) of the car from the point of origin (magnitude only)?
I tried to do x=60sin45 so x=51.054 and y=30%2B60cos45 so y=61.519 then to find the magnitude of displacement I used MagofDis= sqrt%28x%5E2%2By%5E2%29
The answer I got was 6391.137567km but it does not look right.
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You have a triangle with two sides of 30 km and 60 km and the angle of 135° between them.


You need to find the side length d opposite to this angle.


Use the cosine law

     d = sqrt%2830%5E2+%2B+60%5E2+-+2%2A30%2A60%2A%28-sqrt%282%29%2F2%29%29 = 83.938 km  (rounded).    ANSWER

Solved.



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Your process is fine; but obviously 6391km can't be right....

(1) Your calculations for x=60sin%2845%29 and y=30%2B60cos%2845%29 are not correct. sin%2845%29 and cos%2845%29 are the same, so the difference between your x and y should be exactly 30.

(2) After finding x%5E2%2By%5E2, you didn't take the square root, as you said you were going to.