Question

Two cars start moving from the same point. One travels south at 24 mi/h and the other travels west at 18 mi/h. At what rate (in mi/h) is the distance between the cars increasing two hours later

Answer 1

The rate at which the distance between the two cars is increasing is 30 mi/h

Explanation:

Given;

speed of the first car, v₁ = 24 mi/h

speed of the second car, v₂ = 18 mi/h

Two hours later, the position of the cars is calculated as;

position of the first car, d₁ = 24 mi/h x 2 h = 48 mi

position of the second car, d₂ = 18 mi/h x 2 h = 36 mi

The displacement of the two car is calculated as;

displacement, d² = 48² + 36²

d² = 3600

d = √3600

d = 60 mi

The rate at which this displacement is changing = (60 mi) / (2h)

= 30 mi/h