Two cars start moving from the same point. One travels south at mi/h and the other travels west at mi/h. At what rate is the distance between the cars increasing 2 hours later? Round the result to the nearest hundredth.

Question

Two cars start moving from the same point. One travels south at  mi/h and the other travels west at  mi/h. At what rate is the distance between the cars increasing 2 hours later? Round the result to the nearest hundredth.

Quizplus · Accepted Answer

Let's call the distance between the two cars "D". After 2 hours, the car that traveled south would have gone 22 miles (11 mi/h x 2 h), and the car that traveled west would have gone 22 miles (11 mi/h x 2 h) as well.
We can use the Pythagorean theorem to find the value of D:
D= sqrt((22)^2 + (22)^2) ≈ 31.11 miles.
Now, to find how fast the distance between the two cars is increasing, we need to take the derivative of D with respect to time:
dD/dt = (1/D) x (d/D/dt) [(22)^2 + (22)^2]
dD/dt = (1/31.11) x [(2 x 22 x 0) + (2 x 22 x 0)]  (since the rate at which both cars are moving is constant and perpendicular to each other, their dot product is 0)
dD/dt = 0 miles/hour
Therefore, the distance between the two cars is not changing after 2 hours. The answer is C, 11eaa3e5_55e6_8376_9f8f_a30aeb351e17_TB5971_11.

Two Cars Start Moving from the Same Point