Problem 4 - College Physics

Question

\(\bullet\) If you run away from a plane mirror at \(2.40 \mathrm{m} / \mathrm{s},\) at wha speed does your image move away from you?

Step-by-Step Solution

Answer

Your image moves away at 4.80 m/s.

Step 1: Understand the Concept

When you move away from a plane mirror, your image appears to move away as well. The movement of the image in a plane mirror is twice the speed of your motion because the image moves at the same speed in the opposite direction.

Step 2: Calculate Image Speed

Since you move away from the mirror at a speed of 2.40 m/s, your image will also appear to move away from the mirror at 2.40 m/s in the opposite direction. Hence, the speed at which the image moves away from you is twice your speed, 2.40 m/s + 2.40 m/s = 4.80 m/s.

Step 3: Formulate the Result

Combining these insights, we see that both you and your image move apart from their mutual starting point at a combined speed of 4.80 m/s.

Key Concepts

Plane Mirror

A plane mirror is a flat mirror that reflects light, forming images of objects placed in front of it. When light strikes a plane mirror, it bounces back, creating a mirror image that appears to be the same distance behind the mirror as the object is in front. Plane mirrors are unique because they do not magnify or distort images.
They have practical uses such as in bathrooms, dressing rooms, and optical instruments. These mirrors provide a clear, undistorted image, making them ideal for daily visualization and reflection tasks.

Image Speed

In a plane mirror, the speed at which an image appears to move is closely tied to the speed of the object itself. When you move towards or away from the mirror, your image mimics this motion, creating an illusion of movement. Image speed in a mirror is calculated by considering the speed at which you move.
If you're moving away from the mirror at a velocity of 2.40 m/s, your image appears to move at the same speed in the opposite direction. To find out how fast your image seems to move away from you, double the speed of your motion. Therefore, the image speed relative to you is 4.80 m/s in this scenario.

Relative Motion

Relative motion refers to the motion of an object as observed from a particular frame of reference. In the context of a mirror, when you observe your reflection, you are essentially seeing how your movement compares to a stationary background. This means that even if you aren't conscious of your speed, the mirror allows you to perceive it.
When you move at a certain speed towards or away from a mirror, your image reflects that speed back towards or away from you at an equal rate. Understanding relative motion helps in predicting how objects or images move in relation to each other, whether it's in a mirror or in everyday experiences.

Physics Problem Solving

Solving physics problems involving mirrors requires a combination of conceptual understanding and mathematical calculations. Begin by clearly understanding the concept, like how a plane mirror creates twice the apparent motion for an image.
Then, use formulas or logical reasoning to compute the desired quantities, ensuring units are consistent. In this problem, recognizing that the image speed is double your own motion is crucial.

• Break down the problem into smaller parts.
• List known quantities, like speeds.
• Understand the relationship between those quantities.

Finally, formulate the result by combining all insights, ensuring the outcome is logical and aligned with basic principles.