# Solving Ball's Shadow: Theoretical Analysis

• The Rev
However, as the shadow's edge moves further along the curve, its speed rapidly increases until it approaches infinity when it reaches the horizontal part of the curve. The Rev also mentions that this does not contradict relativity as a shadow is not a physical object and cannot transmit information faster than light. They also give an example of a laser beam changing angles and the spot on the moon appearing to move faster than light.
The Rev
Suppose you drop a ball alongside an exponential curve. On the other side of the ball is a continuous light source that is always shining perpendicular to the ball's path, such as in view 1.

As the ball drops, the edge of the balls shadow on the curve moves, while the curve is still vertical, at the speed of the ball, but as the shadow's edge moves further and further along the curve, it rapidly speeds up, as in view 2.

When the shadow's edge approaches the part of the curve that is horizontal, it's speed should approach infinity, as in view 3. However, can it?

$$\infty$$

The Rev

#### Attachments

• view 1.jpg
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• view 2.jpg
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• view 3.jpg
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Yes, a shadow is not a physical object, nor can the faster-than-light speed of the shadow allow us to transmit any information faster than light, so there's no contradiction with relativity here. Similarly, if you shine a laser beam at the moon and change the angle of the beam, the spot on the moon can travel faster than light (even though no individual photon does so)--see here. Also see the superluminal scissors.

That's pretty cool.

$$C$$

The Rev

## 1. How does the shadow of a ball change based on its position in relation to a light source?

The shadow of a ball is dependent on its position in relation to the light source. If the ball is directly in front of the light source, the shadow will be directly behind the ball. As the ball moves to the side of the light source, the shadow will also move to the side, becoming longer or shorter depending on the angle of the light.

## 2. What factors affect the size and shape of a ball's shadow?

The size and shape of a ball's shadow are affected by the distance between the ball and the light source, the angle of the light, and the size and shape of the ball itself. Other factors such as the surface the shadow falls on and any obstructions in the light path can also impact the shadow's appearance.

## 3. Can the shadow of a ball be accurately predicted using mathematical equations?

Yes, the shadow of a ball can be predicted using mathematical equations based on the principles of geometry and optics. These equations take into account the position and size of the ball, the angle and distance of the light source, and other relevant factors to accurately calculate the shape and size of the shadow.

## 4. How can the analysis of a ball's shadow be applied in real-world situations?

The analysis of a ball's shadow has practical applications in various fields such as architecture, photography, and physics. It can help in designing buildings to optimize natural lighting, in setting up lighting for photography, and in understanding the behavior of light in different environments.

## 5. Are there any limitations to the theoretical analysis of a ball's shadow?

While the theoretical analysis of a ball's shadow can provide accurate predictions in ideal conditions, there may be some limitations in real-world scenarios. Factors such as variations in the light source, atmospheric conditions, and the surface the shadow falls on can affect the accuracy of the analysis. Additionally, the shape and texture of the ball may also impact the appearance of the shadow.

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