Example 37
At noon, on a certain day, a truck is 250 mi due east of a car. The truck is traveling west at a constant speed of \( 25 \mathrm{mi} / \mathrm{h} \), while the car is traveling north at \( 50 \mathrm{mi} / \mathrm{h} \).
a. At what rate is the distance between them changing at time \( t \) ?
b. At what time is the distance between the car and the truck neither increasing nor decreasing?
c. What is the minimal distance between the car and the truck?