Question

Traveling at approximately $186,000$ miles per second, about how many miles does a beam of light travel in 2 hours? F. $3.72\times {10}^5$ G. $2.23\times {10}^6$ H. $2.68\times {10}^7$ J. $6.70\times {10}^8$ K. $1.34\times {10}^9$

Short answer

Choose the closest answer among the given options. Options: F: $3.72\times {10}^5$ G: $2.23\times {10}^6$ H: $2.68\times {10}^7$ J: $6.70\times {10}^8$ K: $1.34\times {10}^9$ Answer: K: $1.34\times {10}^9$

Step-by-step solution

Convert the time given (2 hours) to seconds

To convert the time into seconds, we need to multiply the number of hours by 60 for minutes and then 60 again for seconds. Therefore, the conversion is: 2 hours × 60 minutes/hour × 60 seconds/minute = 7200 seconds

Calculate the distance traveled by light using the given speed and the converted time

Now we will use the speed-distance-time relationship to calculate the distance traveled by light. The formula is: distance = speed × time distance = (186,000 miles/second) × 7200 seconds The seconds (time) unit gets canceled out, giving us the distance in miles. distance = $186,000\times 7200$ miles Now let's calculate the total distance: distance = $1,336,000,000$ miles

Comparing the calculated distance to the given options

Now we need to compare the calculated distance of $1,336,000,000$ miles to the provided options. F: $3.72\times {10}^5$ G: $2.23\times {10}^6$ H: $2.68\times {10}^7$ J: $6.70\times {10}^8$ K: $1.34\times {10}^9$ The closest answer to our calculated distance is $1.34\times {10}^9$ miles. Thus, the answer is: K: $1.34\times {10}^9$

Key concepts

Physics Problem Solving

Physics problem solving is a systematic process of understanding and applying physical concepts to find solutions to real-world problems. When faced with a physics problem, such as calculating the distance light travels in a certain period, it is crucial to break down the problem into manageable steps.

First, identify the given data and the physical principles that apply, such as the constant speed of light. Next, determine what needs to be found—in our case, the total distance. Finally, translate this into a mathematical equation or set of equations that can be solved step by step. Critical thinking and a firm grasp of concepts such as units of measurement, conversion factors, and constants are essential components of successful physics problem solving.

Speed-Distance-Time Relationship

Understanding the relationship between speed, distance, and time is an essential component of many physics problems, including those concerning travel and motion. The fundamental equation connecting these three variables is:
$$\text{distance}=\text{speed}\times \text{time}$$

For example, when determining the distance a beam of light travels over a specific duration, one would multiply the speed of light (approximately $186,000$ miles per second) by the total time the light is in motion. Using these precise measurements is necessary to achieve an accurate result. Each variable in this equation is interdependent, which means that if two are known, the third can be calculated.

Scientific Notation

Scientific notation is a way to express very large or very small numbers conveniently, which is particularly useful in fields like physics. It involves writing a number as a product of a decimal number greater than or equal to 1 and less than 10, and a power of 10. For example, the number $1,336,000,000$ can be daunting to read, but in scientific notation, it becomes $1.336\times {10}^9$, which is far easier to interpret and work with.

In the light speed calculation problem, the solution utilizes scientific notation to compare the calculated distance to the provided answers. This notation simplifies calculations and aids in understanding and communicating very large values, like the distances light can travel in vast, empty spaces such as outer space.