Light Waves and Colors Legacy Problem #1 Guided Solution
Problem*
In 1957, the U.S. Naval Research Laboratory conducted the first ever radar measurements of the distance from the Earth to the moon. By reflecting light from an Earth-based source off the moon and measuring the back-and-forth time of transit, scientists determined that the moon is approximately 3.84 x108 m from the Earth. Determine the time it takes light to travel from Earth to the moon and back.
Audio Guided Solution
In this problem radar light is traveling from the earth to the moon and back. The one-way distance from earth to moon is 3.84 times 10 to the 8th meters. What we wish to calculate is the time it takes to travel from the earth to the moon and back. Now to do so we need to know the speed at which light travels through space. At the top of this page it states that unless told otherwise we should use 2.998 times 10 to the 8th meters per second for the speed of light. So using the equation speed equal distance over time we should be able to solve for time. Rearranging time is equal to distance divided by speed. In this question the distance is not the 3.84 times 10 to the 8th meters but the doubling of that distance since the distance we're speaking of is the distance to the moon and back. So we'll double that 3.84 times 10 to the 8th meters and then substitute into the numerator. Divide by 2.998 times 10 to the 8th meters per second. That will give us 2.5617 meters and we can round that to three significant digits.
Solution
2.56 s
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities and record in an organized manner, often times they can be recorded on the diagram itself. Equate given values to the symbols used to represent the corresponding quantity (e.g., \(\descriptive{v}{v,velocity} = \num{3e8}\unit{\meter\per\second}\), \(\descriptive{λ}{λ,wavelength} = 554 \unit{\nano\meter}\), \(\descriptive{f}{f,frequency} = \colorbox{gray}{Unknown}\)).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
Read About It!
Get more information on the topic of Light Waves and Colors at The Physics Classroom Tutorial.