Question

How many minutes does it take light from the sun to reach Earth? (The distance from the sun to Earth is 93 million mi; the speed of light \(=3.00 \times\) \(\left.10^{8} \mathrm{~m} / \mathrm{s} .\right)\)

Short answer

Approximately 8 minutes and 20 seconds. Further accuracy would depend on precise calculations and rounding off.

Step-by-step solution

Convert Distance to Meters

First, it is necessary to convert the distance between the Earth and the Sun from miles to meters because the speed of light is given in meters per second. As 1 miles is equivalent to approximately 1609.34 meters, therefore our conversion would be: \(93,000,000 \, mi = 93,000,000 \times 1609.34 \, m \).

Calculate Time

Next, divide the converted distance by the speed of light to get the time in seconds. The formula of time (\(t\)) is given as: \(t = \frac{distance}{speed}\), substituting the known values, the calculation would be: \(t = \frac{93,000,000 \times 1609.34 \, m}{3.00 \times 10^{8} \, m/s}\)

Convert Time to Minutes

In the previous step, the time is calculated in seconds, to convert this into minutes use the fact that 1 minute equals 60 seconds. Hence, divide the calculated time by 60: \(t_{minutes} = \frac{t_{seconds}}{60}\)

Key concepts

Distance Conversion

When solving physics problems, distance conversion is a crucial step, especially when dealing with various units of measurement. It's common for distances to be provided in one unit, like miles, but the calculations require another, such as meters. This unit consistency is essential to ensure that formulas and calculations remain accurate and meaningful.
To convert distances from miles to meters, we rely on the conversion factor that 1 mile equals approximately 1609.34 meters. This is a fixed value that serves as a universal constant across physics and science.
For example, if the distance from the sun to Earth is 93 million miles, converting that into meters requires multiplying 93,000,000 by 1609.34. This systematic approach simplifies the process, allowing for correct calculations when integrated into formulas dependent on the metric system.

Physics Problem Solving

In physics, problem solving often involves breaking down a problem into understandable steps. An effective strategy to solve physics problems is to:

• Identify what is being asked and what information is given.
• Decide which physical principles and formulas apply.
• Perform necessary calculations in an organized manner.
• Verify the results for consistency and accuracy.

For the problem of calculating how long light takes to travel from the sun to Earth:

• We know the distance and the speed of light are given.
• By applying the formula for time, \[t = \frac{distance}{speed}\], the time it takes for light to reach the Earth can be determined. This formula comes from a basic principle of motion that relates distance, speed, and time.

Problem solving in physics often boils down to applying fundamental principles together with logical reasoning and mathematical calculations.

Unit Conversion in Physics

Unit conversion is a fundamental skill in physics, ensuring that calculations align with the units required by specific formulas. In physics, using consistent units allows for smooth computation and accurate interpretation of results.
For instance, when dealing with the speed of light, which is typically given in meters per second (m/s), any accompanying measurement like distance should also be in compatible units, here that means meters. This means:

• Convert all distances to meters when working with meters per second.
• Ensure time is in seconds when using calculations derived from this unit speed.

The process is simple: apply the correct conversion factors—for instance, converting miles to meters as outlined in distance conversion. Once calculations yield a result in a base unit, further conversions can translate seconds into minutes, as needed, maintaining clarity and precision in the final answer. Such meticulous conversions underpin accurate and reliable physics problem solving.