A car travels 10 km southeast and then 15 km in a direction 60 degrees northeast. Find the magnitude of the cars resultant vector in km.

Answer 1

1) Express the vectors in terms of the traditional math angle 10 km at -45° and 15 at 60°.

2) Add the vectors components in order to find the components of the resultant vector:

d_x = 10cos(-45) + 15cos(60) = 5sqrt(2) + 15/2 = 14.5711 km

d_y = 10sin(-45) + 15 sin(60) = -5sqrt(2) + 15sqrt(3)/2 = 5.9193 km

I left the answers in terms of radicals because math class vs. physics class.

|d| = sqrt(d_x² + d_y²) is the answer

This will be a pain without using a calculator, so you're probably better off using it from the beginning.

Please consider a tutor. Take care.