And Another Vertex problem

oriont

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May 21, 2011
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Problem reads: A truck is traveling due north at 30km/hr towards a crossroads. On a perpendicular road a police car is traveling west toward the intersection at 40km/hr. both vehicles will reach the crossroads in exactly one hour. find the vector representing the displacement of the truck with respect to the police car.

What I know: (maybe)

The vector is part of an isosceles triangle with 90° where the vectors meet and 45° where the vectors start.

What I don't know:

Whats next?
 
Why is it isosceles?

How far does each travel in that hour?
 
Pretty sure I got that one figured out. Its not an isosceles triangle.

just used the Pythagorean which came out to be ?(40^2+30^2) which comes out to 50KM. I then used the law of sines sin90°/50=sin b/30 which comes out to 36.78°
 
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