Question

The speed of sound in air is 320 meters per second. If you see a flash of lightning and it takes 8 seconds before you hear the thunder, how many kilometers away was the lightning strike? (Assume that the light reaches you instantly.) (A) 2.56 kilometers (B) 4 kilometers (C) 40 kilometers (D) 2560 kilometers

Short answer

The lightning strike was \(2.56\) kilometers away. The correct answer is (A) \(2.56\) kilometers.

Step-by-step solution

Write down the given information

The speed of sound in air is 320 m/s and the time taken to hear the thunder after seeing the lightning flash is 8 seconds.

Calculate the distance

Use the formula: distance = speed × time. Distance = 320 m/s × 8 s

Solve for distance

Calculate the distance: Distance = 320 m/s × 8 s = 2560 meters

Convert the distance to kilometers

Since 1 kilometer = 1000 meters, Convert the distance to kilometers: Distance = 2560 meters ÷ 1000 Distance = 2.56 kilometers

Identify the correct answer

Compare the calculated distance to the options provided: (A) 2.56 kilometers (B) 4 kilometers (C) 40 kilometers (D) 2560 kilometers The correct answer is (A) 2.56 kilometers, which matches the distance calculated in Step 4.

Key concepts

Speed of Sound Calculation

When we talk about the speed of sound, we're referring to how quickly sound waves travel through a medium, such as air, water, or steel. The speed of sound is not constant and can vary with the medium's temperature, density, and pressure. For our educational purposes, we typically use standard conditions to simplify the calculations.

In the given exercise, the speed of sound in air is provided as 320 meters per second (m/s). This integer is crucial in calculating the distance of occurrences such as a lightning strike. When you see light from the lightning, the light reaches you nearly instantly because it travels much faster than sound. However, sound has a finite speed, and there will be a delay before you hear the thunder after seeing the flash. By measuring this time and knowing the speed of sound, you can calculate the distance to the lightning strike using the time it took for the sound to reach you.

This scenario can also be related to practical situations such as determining your location using echolocation or recognizing the distance to an object by sound. Understanding how to calculate with the speed of sound prepares students for real-world applications where time and distance calculations are essential.

Distance Formula

The distance formula is a fundamental expression used in physics to determine how far something has traveled. At its core, the distance formula is quite straightforward:

Distance = Speed × Time

For example, if a vehicle is moving at a constant speed of 60 kilometers per hour for 2 hours, it has traveled a distance of 120 kilometers.

It is paramount, especially for GED math practice, to internalize this formula as it links together three key aspects of motion: speed, distance, and time. In the context of the original exercise, we apply this formula to sound, calculating how far the sound of thunder has traveled in a given time. By using the formula with the speed of sound given and the time delay between the lightning and the thunder, you can find out how far away the lightning struck.

The distance formula isn’t just useful for calculations on paper; it’s a practical tool for scientific investigations, engineering, and everyday problem solving.

Unit Conversion

An often overlooked but crucial skill in mathematics and science is unit conversion. Many students can stumble on problems not because they don't understand the concepts but because they overlook the importance of units in their calculations.

In the context of our exercise, after calculating the distance the sound traveled, it's essential to convert the result from meters to kilometers to match the option units given. The relationship between meters and kilometers is a basic conversion, where 1 kilometer equals 1000 meters. To convert meters to kilometers, you divide the number of meters by 1000:

Kilometers = Meters ÷ 1000

This process is applicable to various scenarios, such as converting inches to centimeters or pounds to kilograms. Mastery of unit conversions is not only essential for passing exams but is also extensively used in fields such as science, engineering, medicine, and many others, often requiring precise measurements and the ability to communicate findings or perform tasks using different unit systems.

For GED math practice, encountering unit conversions is common, so understanding how to perform them accurately is key to solving many kinds of numerical problems.