Question

4. Two cars are starting from positions that are 20 miles apart. They are both headed for the same intersection, as depicted in the diagram below. Car A is traveling at 30 mph, and Car B is traveling at 45 mph. Which car will reach the intersection first? Part I: Use the law of cosines to determine how far Car B has to travel to reach the intersection. (2

Answer 1

For this case, the first thing to do is to use the law of cosine to determine the distance from B to the intersection.
 We have then:$d = 18 ^ 2 + 20 ^ 2 - 2 * 18 * 20 * cos (95) d = \sqrt{18 ^ 2 + 20 ^ 2 - 2 * 18 * 20 * cos (95)} d = 28.05$
 Then, we know that by definition:
 t = d / v
 Where,
 t: time
 d: distance
 v: speed
 For car A we have:
 $ta = 18/30 ta = 0.6 hours$
 For car B we have:
 $tb = 28.05 / 45 tb = 0.62 hours$
 Answer:
 car A will reach the intersection first