Two cars start moving from the same point. One travels south at 30km/h and the other travels west at 40km/h. At what rate is the distance between the cars increasing two hours later and show the diagram?
Let's denote the distance between the two cars as D, and let t be the time in hours.
After two hours, the car travelling south has traveled 30km/h * 2h = 60km.
After two hours, the car travelling west has traveled 40km/h * 2h = 80km.
Using the Pythagorean theorem, we can calculate the distance between the two cars at any given time t:
D^2 = (80km)^2 + (60km)^2
D^2 = 6400km^2 + 3600km^2
D^2 = 10000km^2
D = 100km
The distance between the two cars is 100km after two hours.
To find the rate at which the distance is increasing two hours later, we can differentiate the distance equation with respect to time t:
2D(dD/dt) = 0
dD/dt = 0km/h
This means that the distance between the two cars is not changing, and therefore the rate at which the distance is increasing two hours later is 0km/h.
Here is the diagram:
```
C (car travelling south)
|
|
| 100km
--------------------- B
|
|
(car travelling west)
A
```