Question

How many nanoseconds does it take light to travel 1.00 ft in vacuum? (This result is a useful quantity to remember.)

Short answer

Approximately 1.017 nanoseconds.

Step-by-step solution

Understand the Speed of Light

First, note that the speed of light in a vacuum is a fundamental constant, approximately \( c = 299,792,458 \) meters per second (m/s).

Convert 'feet' to 'meters'

We need to convert 1.00 ft to meters. Using the conversion, \(1 \text{ ft} = 0.3048 \text{ m}\), we find: \[1.00 \text{ ft} = 0.3048 \text{ meters}.\]

Calculate Time in Seconds

Using the formula for speed, \( v = \frac{d}{t} \), where \( d \) is distance and \( t \) is time, we rearrange to find time:\[ t = \frac{d}{v}.\]Substituting the values, \(d = 0.3048 \text{ m}\) and \(v = 299,792,458 \text{ m/s} \), we get:\[ t = \frac{0.3048}{299,792,458} \approx 1.0167038 \times 10^{-9} \text{ seconds}.\]

Convert Time to Nanoseconds

Since we want the time in nanoseconds, remember that \(1 \text{ ns} = 10^{-9} \text{ s}\). Therefore, \[ t = 1.0167038 \text{ ns}.\]

Key concepts

Speed of Light

The speed of light is one of the fundamental constants in physics, denoted by the symbol \( c \). It's known to be approximately \( 299,792,458 \) meters per second (m/s) when traveling through a vacuum. Light travels incredibly fast, and this speed is crucial in areas like astronomy and electronics.
It represents the maximum speed at which information and matter can travel. Understanding this speed helps us calculate a variety of scenarios, from everyday phenomena to complex scientific processes.
Fun fact: because light is so fast, it can travel around the Earth's equator 7.5 times in just one second!

Unit Conversion

Unit conversion is a vital skill in physics, enabling us to switch between different measuring systems. For this exercise, we convert feet to meters because the speed of light is given in meters per second.

• 1 foot is equivalent to 0.3048 meters
• By multiplying 1.00 ft by 0.3048, we convert it to meters

Understanding unit conversion allows you to work seamlessly across various problems and ensures the accuracy of your scientific calculations.
Always double-check conversion factors, as mistakes can easily lead to errors in final answers.

Time Calculation

To find out how long it takes for light to travel in a vacuum, we use the formula \( t = \frac{d}{v} \), where \( d \) is the distance and \( v \) is the velocity or speed.
In our exercise, we had to determine the time for light to travel 0.3048 meters (converted from feet) at its incredible speed of \( 299,792,458 \) m/s. Plugging these values into the formula gives us the time:
\[ t = \frac{0.3048}{299,792,458} \approx 1.0167038 \times 10^{-9} \text{ seconds} \]
This quick calculation tells us the journey for light over a very short distance takes only a billionth of a second.

Scientific Notation

Scientific notation is a way to express very large or very small numbers in a more manageable form. It's especially useful in physics when dealing with extremes like the speed of light or atomic scales.
In this case, the time for light to travel a foot is approximately \( 1.0167038 \times 10^{-9} \) seconds. This notation helps simplify numbers by indicating how many times to multiply by ten.

• The exponent \( -9 \) tells us to move the decimal point nine places to the left.
• It makes complex calculations easier to read and understand.

Grasping scientific notation is crucial for tackling many physics problems efficiently.