Question

Two cars are travelling east along a straight highway at the same speed. At an intersection, the highway branches and splits into two straight roads, one heading approximately north-east and one heading approximately south-east. The angle betwen the two roads is 60 degrees. The two cars leave the intersection at the same time, one travelling north-east at 100 km/h and the other travelling south-east at 80 km/h. How fast is the distance between the two cars changing 30 minutes after they leave the intersection.

Answer 1

using the law of cosines, the distance z at time t hiours is
z^2 = (100t)^2 + (80t)^2 - 2(100t)(80t)cos60° = 8400t^2
z = 10√21 t
dz/dt is a constant 10√21 km/hr

Answer 2

so how would I find how fast the distance is changing 30 min after they leave the intersection?

Answer 3

and I got z = 10√84t