A car is driven 125 km west and then 80 km southwest. What is the displacement of the car from the point of...?
A car is driven 125 km west and then 80 km southwest. What is the displacement of the car from the point of origin (magnitude and direction)?
degrees south of west ?
- 1 decade agoBest Answer
Use the cosine rule. Drawing out the vectors (first draw a line 125km west, then attach a line 80km to the end of it at an angle of (180-45=)135degrees). You can then use the cosine formula a^2=b^2 + c^2 - 2bcCOSA. This will give you the magnitude (the line joining the two lines in the diagram). The direction is simple -22.5 degrees to the horizontal as you have drawn an isoceles triangle.
- SteveLv 71 decade ago
D = √[125² + 80² - 2*80*125*cos135°]
Θ = arcsin[80*sin135°/D]