Grade 11 · Science · Physics

11th grade The speed of light and relativity worksheet

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The speed of light and relativity

Grade 11 Science Worksheet - Challenge Me

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Circle the best answer, or write your answer on the line.

A muon lives 2.197 μs at rest and moves at 0.999c, where c = 299.792458 m per μs. Using t = γt₀, how far does it travel in one lifetime, to the nearest m, Esme?
2.
Jun says relativity has no practical use in daily life. Agree or disagree?
- Agree: GPS works without it
- Disagree: GPS depends on it
- Agree: clocks can't detect it
3.
Kira says time dilation just means fast clocks are broken. Agree or disagree?
- Agree: cold slows the clocks down
- Agree: high speed damages the clocks' gears
- Disagree: time itself runs differently
4.
Luz says a muon would notice its own life stretched. Agree or disagree?
- Agree: it feels 10 times longer
- Agree: it feels its time stop completely
- Disagree: it lives 2.197 μs in its frame
Read this first
GPS satellite clocks compared with ground clocks (from Ashby's fractional rates × 86,400 s)
Effect Change in the satellite clock (μs per day)
Weaker gravity at its height +45.7
Its orbital speed -7.1
Net +38.6
5.
Using the table, if the net 38.6 μs a day weren't corrected, about how far would positions drift each day, Milo?
- About 11.6 km
- About 0.1 km
- About 116.0 km
6.
Using the table, how are GPS satellite clocks set before launch, Noah?
- Slightly slow on the ground
- Slightly fast, to add to the effect
- They aren't adjusted at any point
7.
Using the table, which effect is bigger for a GPS clock, Pia?
- Weaker gravity, about 6 times bigger
- Orbital speed, about 6 times bigger
- They are equal in size
8.
At 0.1c, γ is about 1.005. What does this say about everyday speeds, Ren?
- Clocks run at half speed
- Lengths double at them
- Time dilation is tiny at them
9.
At about what speed is γ equal to 2, Tala?
- About 0.87c
- Half of c, 0.5c
- Twice c, 2c
10.
Speed rises from 0.9c to 0.99c. What happens to γ, Zee?
- It about triples
- It rises by about 10%
- It falls a little

Effect	Change in the satellite clock (μs per day)
Weaker gravity at its height	+45.7
Its orbital speed	-7.1
Net	+38.6

11th grade The speed of light and relativity worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

The speed of light and relativity. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can say that every observer measures the same speed for light, c = 299,792,458 m/s, and that nothing with mass reaches it.
I can find γ = 1 ÷ √(1 − v²/c²) and use t = γt₀: a moving clock runs slow, and a moving object is shorter along its motion.
I can explain why fast muons from high in the air reach the ground.
I can read GPS clock effects: weaker gravity makes satellite clocks gain 45.7 μs a day, their speed makes them lose 7.1 μs, and the net is +38.6 μs.

Standard: none (FL)

Words to know

frame of reference: The point of view, moving or still, that measurements are made from

time dilation: A moving clock measured as ticking slower

length contraction: A moving object measured as shorter along its motion

γ (gamma): 1 ÷ √(1 − v²/c²); 1 at rest, larger near c

muon: A heavier cousin of the electron that decays in about 2.2 μs

Common mistakes

Your child left out the square root. γ = 1 ÷ √(1 − v²/c²).

Your child divided by γ. A moving clock runs slow, so its lifetime looks longer: t = γt₀.

Your child used the muon's rest lifetime. From the ground, its lifetime is stretched by γ, so it travels farther.

Questions parents ask

What is the most common mistake with the speed of light and relativity?

Your child left out the square root. γ = 1 ÷ √(1 − v²/c²).

Are these 11th grade science worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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