Question

A car travels down a highway at 25m/s. An observer stands 150m from the highway. How fast is the distance from the observer to the car increasing when the car passes in front of the observer? Explain your answer without making any calculations.

Answer 1

When the car passes directly in front of the observer, the rate at which the distance from the observer to the car is increasing is 0 m/s.

Step-by-step explanation:

The question is asking about the rate at which the distance between the observer and the car is increasing when the car passes in front of the observer. Since the car is traveling parallel to the observer at 25 m/s, and at the closest point, the car is directly opposite to the observer, the distance between the car and the observer does not change at that instant. Therefore, when the car is at the point closest to the observer, the rate at which the distance is increasing is 0 m/s.

This is a concept from relative velocity and it illustrates the scenario when two objects are in perpendicular motion relative to each other. At the instant the car is closest to the observer, the component of the car's velocity that would increase the distance between them is zero, because the car is not moving away or towards the observer but rather alongside the line that connects them.