# Math Help - Vertex problem

1. ## Vertex problem

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?

2. distance = speed * time.

so the police car starts 40km from the cross-roads, the truck stars 30km away.

Can you use that information to find the displacement vector?

3. Originally Posted by oriont
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?
Dear oriont,

Since the truck travels at 30km/hr and takes one hour to reach the crossroads;

Distance from the crossroads to the truck= $30km/hr\times 1hr=30km$

Since the police car travels at 40km/hr and takes one hour to reach the crossroads;

Distance from the crossroads to the police car= $40km/hr\times 1hr=40km$

Please refer to the attached figure. You will see that the resultant vector representing the displacement is 30 km in length and directed from east to north by an angle of 36.9 degrees.

Hope you understood.

4. Yes makes perfect sense, thank you.