Question 155178
The car headed north at 50 km/hr will have traveled a distance of 100km after 2 hours, right? ((2hrs)*(50km/hr) = 100km.
The car headed east at 70 km/hr will have traveled 140km after 2 hours, ok? (2hrs)*(70km/hr) = 140km.
So you now have two legs of a right triangle in which the base is a vector of magnitude 140km and the height is a vector of magnitude 100km.
The distance between the two cars, after 2 hours of travel, is represented by the hypotenuse of this right triangle.
So you can call upon Pythagoras {{{c^2 = a^2+b^2}}} to help find the length (distance vector) of the hypotenuse (d).
{{{d^2 = (140)^2+(100)^2}}}
{{{d^2 = 19600+10000}}}
{{{d^2 = 29600}}}
{{{d = sqrt(29600)}}}
{{{d = 172}}}km.  Approximately.
This would be a vector whose magnitude is 172.