Question

. Science Light travels approximately \(1,860,000\) miles in 10 seconds. How long will it take light to travel the \(93,000,000\) miles from the sun to Earth?

Short answer

It takes light 500 seconds to travel from the sun to Earth.

Step-by-step solution

Identify the given information

We are told that light travels 1,860,000 miles in 10 seconds and we need to find out how long it will take light to travel 93,000,000 miles.

Determine the speed of light

To find the speed of light, calculate how many miles light travels in one second. Since light travels 1,860,000 miles in 10 seconds, we divide by 10 to find the distance traveled in one second: \( \frac{1,860,000 \text{ miles}}{10 \text{ seconds}} = 186,000 \text{ miles per second} \).

Calculate the time to travel 93,000,000 miles

With the speed of light found, we now calculate the time it takes to travel 93,000,000 miles. Using the formula \( \text{time} = \frac{\text{distance}}{\text{speed}} \), we have: \( \text{time} = \frac{93,000,000 \text{ miles}}{186,000 \text{ miles per second}} \).

Solve for time

Perform the division: \( \frac{93,000,000}{186,000} = 500 \). Thus, the time it takes for light to travel from the sun to Earth is 500 seconds.

Key concepts

Distance Calculation

When thinking about distance, it's simply how far one point is from another. To calculate the distance, you often need to know the speed of the object—how fast it's moving—and the time over which it travels. In problems involving the speed of light, it becomes particularly interesting because light covers a substantial distance very quickly. In our example, we need to know how far light travels so we can decide how long it takes to travel from the sun to Earth. We know light journeys a staggering 93,000,000 miles to reach us.

Here's how we can utilize distance calculations in this context:

• Understand the total distance (93,000,000 miles in this scenario).
• Break down the distance into smaller intervals if needed, although light's consistent speed simplifies our task.
• Relate the distance directly to both speed and time for a complete picture.

Once you grasp the concept that distance is dependent on speed and time, disentangling these two for calculations becomes straightforward. You can visualize this by imagining light as a runner covering a track in a certain time while maintaining a constant speed.

Time Calculation

Time calculations allow us to compute how long an event or journey takes. This is especially significant in scenarios involving tremendous speeds, like the speed of light. With a simple formula, we can determine time if we know both the speed and distance. Given that light moves at 186,000 miles per second, we use this rate to find out how much time it will take to complete 93,000,000 miles from the sun to Earth. The formula for time, derived from the basic physics principle, is:

• Time = \( \frac{\text{Distance}}{\text{Speed}} \) .

Insert the known values:

• Distance: 93,000,000 miles
• Speed: 186,000 miles per second

The calculation then becomes \( \frac{93,000,000}{186,000} \), which results in 500 seconds. Break down the problem to ensure each number input is clear and correct, as this ensures you avoid common mistakes. Understanding time calculations leads to better insights into motion and how different factors impact duration.

Physics in Geometry

Physics often utilizes geometric principles to elucidate various phenomena, including the movement of light. Geometry, the foundation of space and volumes, plays a crucial role in calculating paths, speeds, and distances in various contexts. Light typically travels in straight lines, much like vectors in geometry, which lets us use geometric calculations to predict and measure its path. In our scenario, the distance from the sun to Earth is measured along a straight line. This makes it easier to apply physics calculations using straightforward geometric understandings:

• Recognize the path of light as a geometric line segment.
• Fold in physics principles to understand speed and time against this geometric path.
• Utilize geometry to visualize and solve physics problems more effectively.

By blending physics with geometry, you gain a dual advantage of spatial and kinematic understanding, letting you tackle complex problems with more tools at your disposal. This method benefits both conceptual understanding and practical problem-solving in real-world scenarios.