Question

It was a dark and stormy night, when suddenly you saw a flash of lightning. Three-and-a-half seconds later you heard the thunder. Given that the speed of sound in air is \(340 \mathrm{~m} / \mathrm{s}\), how far away did the lightning bolt strike? Give your answer in both meters and kilometers.

Short answer

The lightning bolt struck 1190 meters away, or 1.19 kilometers away.

Step-by-step solution

Understand the problem

We need to find out the distance from the observer to the lightning strike. We know the time between seeing the lightning and hearing the thunder is 3.5 seconds and the speed of sound is \(340 \, \text{m/s}\).

Use the formula for distance

To calculate the distance, use the formula: \(\text{distance} = \text{speed} \times \text{time}\). Here, the speed of sound is \(340 \, \text{m/s}\) and the time is \(3.5 \, \text{s}\).

Calculate the distance in meters

Substitute the given values into the formula: \(\text{distance} = 340 \, \text{m/s} \times 3.5 \, \text{s}\). Performing the multiplication gives \(\text{distance} = 1190 \, \text{m}\).

Convert meters to kilometers

To convert meters to kilometers, divide the distance in meters by 1000: \(\text{distance in km} = \frac{1190}{1000} = 1.19 \, \text{km}\).

Key concepts

Distance Calculation

Calculating distance can be a fun and practical application of physics. When you see lightning but hear thunder a few seconds later, you are experiencing this concept firsthand! To calculate how far the lightning struck from you, you must know the time it took for the sound to travel and the speed of sound in that medium, which is the air for this scenario.

The famous formula to determine distance is:

• Distance = Speed × Time

Using this formula means you determine how many meters the sound travels each second after the lightning flash. You multiply this rate (or speed) by the number of seconds it takes for you to hear the thunder.

In our original exercise, the time is 3.5 seconds, and we know the speed of sound is 340 m/s. Plug these values into the formula:
\[\text{Distance} = 340 \, \text{m/s} \times 3.5 \, \text{s}\]Doing the calculation yields:
\[\text{Distance} = 1190 \, \text{meters}\]The sound of thunder took 3.5 seconds to travel 1190 meters, showing how this back-of-the-envelope calculation accurately represents your proximity to the original lightning flash.

Unit Conversion

Unit conversion is an essential skill in physics, often helping bridge the gap between measurements and practical use of results. In the context of our original exercise, after calculating the distance in meters, we convert it to kilometers. Why? Because talking in kilometers can be more intuitive for distances over a thousand meters.

To convert meters to kilometers, remember:

• 1 kilometer = 1000 meters

This means you divide the number of meters by 1000 to get the number in kilometers:
\[\text{Distance in km} = \frac{1190}{1000} = 1.19 \, \text{km}\]So, the lightning struck approximately 1.19 kilometers away. Converting units helps give a clearer, often more relatable understanding of measurements. Whether you are dealing with distances, weights, or volumes, knowing how to switch between units is incredibly beneficial.

Physics Problem Solving

Physics problem-solving is like untangling a puzzle. This involves identifying what information you have, what the question asks, and then applying the right formulas and knowledge. The original exercise is a classic example of a physics problem where you apply theory to practical observation.

Here's a step-by-step reflection on problem-solving through physics:

• Identify Key Information: Gather the given data (like speed of sound and time here) and what you need (the distance).
• Choose the Right Formula: Use the suitable physics equation— in this case, Distance = Speed × Time.
• Perform Calculations: Substitute values into formulas and solve.
• Conclude with Conversion: Convert results into relevant units so they are meaningful (like converting meters to kilometers).

Physics problems become easier when broken down like this. It transforms a daunting task into a manageable series of logical steps, providing clarity and understanding.