# Velocity of Separation: How fast is the distance between two cars changing?

**Problem**

A Toyota Land Cruiser drives east from point *A* at 30 kph. Another car, Ford Expedition, starting from *B* at the same time, drives S30°W toward *A* at 60 kph. *B* is 30 km from *A*. How fast in kph is the distance between two cars changing after 30 minutes? Hint: Use the Cosine Law.

A. 70 kph | C. 55 kph |

B. 80 kph | D. 60 kph |

**Answer Key**

[ D ]

**Solution**

After 30 min., the Ford Expedition is exactly at

*A*.

$v_\text{separation} = v_{Fx} + v_T$

$v_\text{separation} = 60 \cos 60^\circ + 30$

$v_\text{separation} = 60 ~ \text{kph}$

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