A car is driven 225 km West then 98 km Southwest (45 degrees). What is the displ

Question

A car is driven 225 km West then 98 km Southwest (45 degrees). What is the displacement of the car from the point of origin (magnitude and direction)? Draw a diagram.

(We are working with adding vectors, so I assume I'd be finding the Ax, Ay, Bx, By values by using Cos and Sin, then usng the Pythagorean Theorem to solve for the third line of the triangle "R", then using inverse Tan to find the Degree. My interpretation of how the lines on the graph doesn't look right though and I'm not sure if I'm even approaching this right.) Thanks!

Explanation / Answer

displacement = -225 i + 0 j

displacement = 98 * cos 225º i + 98 * sin 225º j = -69.286 km i - 69.286 km j

total displacement = -294.286 km i - 69.286 km j

magnitude of displacement = sqrt [ 294.2862 + 69.2862 ] km

= 302 km

theta = arctan(-69.286 / -294.286)

= 13.22º S of West

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