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In this exercise, the speed of sound is a crucial part of determining how far the airplane is from an observer. Typically, the speed of sound in dry air at 20 degrees Celsius is about 343 meters per second or roughly 1125 feet per second. However, for this specific exercise, we've rounded it to 1100 feet per second. Variations might happen due to humidity or temperature changes.
When you hear thunder after seeing a lightning flash, it's because the sound takes longer to travel. Sound waves move much slower than light waves, so there's often a noticeable delay. By using the speed of sound, you can calculate the distance of an object based on how long it takes for sound to travel from it to you. Use the formula:

• Distance = Speed of Sound imes Time

So, if you know the speed and how long the sound took to reach you, you can deduce the distance. In this case, multiplying 1100 ft/s by 5.0 seconds gives a distance of 5500 feet.

The speed of light is incredibly fast compared to sound. In air, light typically travels at around 983,571,088.9 feet per second. This speed is so great that for short distances, like seeing a light from a lightning strike, it's essentially instantaneous to the human eye.
Because of this, when calculating the distance to something using sound, you can usually ignore the time it takes for light to travel over the same distance. Unlike sound, light waves don't slow significantly when passing through air, making them far superior for instantaneous signal detection. For our exercise, this means we can focus on the sound delay without worrying about the light delay. That explains why we haven't included the speed of light in those calculations. Its contribution to the delay is practically meaningless in human experience in situations like these.

Understanding how to calculate distance and velocity is fundamental in physics. Distance is how far an object has moved, calculated with formulas involving speed and time. Velocity, however, not only considers speed but also the direction.In our exercise:

• First, we calculated the distance from the observer to the plane at the time of lighting using the speed of sound and time delay.
• Next, the plane's velocity was determined by dividing the distance by the time taken (15 seconds, here).

The formula for velocity is:

• Velocity = \( \frac{Distance}{Time} \)

By applying this method, we found the plane's velocity to be approximately 367 ft/s. These calculations demonstrate how closely related understanding of distance, speed, and time is when solving physics problems.