Two straight roads diverge at an angle of 45â°. two cars leave the intersection at 2: 00 p. m., one traveling at 36 mi/h and the other at 52 mi/h. how far apart are the cars at 2: 30 p. m.?

Let's take the x-axis as the direction of car 1, which is traveling at speed . Car 2 is traveling at speed  in a direction of  with respect to the x-axis.

Let's start by finding the distance covered by the two cars in between 2.00 pm and 2.30 pm, so in 30 minutes. We can write 30 minutes as 0.5 hours, so . The distance covered by the two cars is


 S1 lies on the x-axis, while we have to decompose S2 on both axes:



Assuming the two cars started their motion from the origin of the axes (0,0), then we can rewrite the final coordinates of the two cars as
- car 1: (18 mi,0)
- car 2: (18.4 mi, 18.4 mi)
And so the distance between the two cars will be

The third hammer 8 pounds