A car is driven 165 km west and then 95 km southwest. What is the displacement of the car from the point of origin (magnitude and direction)? (physics)

Guest Sep 25, 2014

#1**+11 **

We have two vectors here, v_{1} and v_{2 }

v_{1} = <165cos180, 165sin180> and v_{2} = <95cos(225), 95sin(225)>

Summing the "x" components we have

165cos(180) + 95cos(225) = about -232.18

Summing the "y" components we have

165sin(180) + 95sin(225) = about -67.18

And the magnitude is given by √[(-232.18)^{2} + (-67.18)^{2}] = about 241.7 km

And the direction is given by

tan^{-1} (-67.18/-232.18) = about 16.14° in the 3rd quadrant = about 196.14°

CPhill
Sep 25, 2014

#1**+11 **

Best Answer

We have two vectors here, v_{1} and v_{2 }

v_{1} = <165cos180, 165sin180> and v_{2} = <95cos(225), 95sin(225)>

Summing the "x" components we have

165cos(180) + 95cos(225) = about -232.18

Summing the "y" components we have

165sin(180) + 95sin(225) = about -67.18

And the magnitude is given by √[(-232.18)^{2} + (-67.18)^{2}] = about 241.7 km

And the direction is given by

tan^{-1} (-67.18/-232.18) = about 16.14° in the 3rd quadrant = about 196.14°

CPhill
Sep 25, 2014