A car is driving east for a distance of 50km, then north for 30km and then in a direction 30 east of north for 25km. Determine the angle of the car's total displacement from its starting point?

1 Answer
Richard G.
Oct 12, 2015

Break each vector component into its constituent parts (N/S & E/W), then add them all. Vector 3 needs a trigonometry calculation.

Vector 1: 0 km North/South, 50 km East/West
Vector 2: 30 km North/South, 0 km East/West
Vector 3: cos 30 x 25 = 21.65 km N/S, sin 30 x 25 = 12.5 km E/W

The sums: 51.65 km N/S, 62.5 km E/W

Using trigonometry again, tan = opp./adj. = 62.5km/51.65km = 1.21
Turning this into an angle, you get 50.4 degrees East of North

Related questions
Impact of this question
18195 views around the world
You can reuse this answer
Creative Commons License