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

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

A muon at rest lives 2.197 μs on average (PDG). Measured from the ground, how long does one moving at 0.995c last, to 0.01 μs, Bo?
A muon at rest lives 2.197 μs on average (PDG). Measured from the ground, how long does one moving at 0.98c last, to 0.01 μs, Esme?
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
3.
Using the table, does a GPS satellite clock run fast or slow overall, compared with ground clocks, Jun?
- Slow, by about 38.6 μs a day
- The two effects cancel exactly
- Fast, by about 38.6 μs a day
4.
Using the table, why does the satellite's speed make its clock lose time, Kira?
- Its batteries run down
- Moving clocks tick slower
- Space is colder than the ground
5.
Using the table, why does the satellite's height make its clock gain time, Luz?
- Its speed makes it run fast
- It is closer to the Sun
- Gravity is weaker up there
6.
A rod moves past at 0.8c. Measured from the ground, how long is it along its motion, Milo?
- Longer than at rest
- Shorter than at rest
- Exactly as long as at rest
7.
Muons made high in the air reach the ground in large numbers. Why, Noah?
- They travel faster than light
- Their lifetimes are stretched
- Air makes them live longer
8.
Two matched clocks: one rides a fast rocket and returns, one stays put. Ignoring gravity, which shows less time, Pia?
- They show the same time
- The one that rode the rocket
- The one that stayed put
9.
As an object gets close to c, what happens to the energy needed to speed it up more, Ren?
- It stays the same
- It drops to zero
- It grows without limit
10.
Sunlight takes about 499 seconds to reach Earth. What does this show, Zee?
- Sunlight slows down in space
- Light's speed is finite
- Light arrives instantly

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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