Calculus Question

Question

Two cars start moving from the same point. one travels south at 30 mi/h and the other travels west at 70 mi/h. At what rate is the distance between the cars increasing 4 hours later?

Answer 1

The rate the distance between the cars increasing is just the vector sum of their velocities. This rate doesn't depend on the distance between the cars at a given point in time.

Since velocity vector directions are 90° apart, their vector sum is calculate using the Pythagorean theorem.

v = √(v_s² + v_w²) = √((30)² + (70)²) = √(5800) = 10√58