The speed of light and relativity

Answer Key - Grade 11 Science Worksheet - Challenge Me

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

1. 1.

   A muon lives 2.197 μs at rest and moves at 0.99c, where c = 299.792458 m per μs. Using t = γt₀, how far does it travel in one lifetime, to the nearest m, Ari?

   4622 m
2. 2.

   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?

   14,717 m
3. 3.

   Jun says relativity has no practical use in daily life. Agree or disagree?

   • Agree: GPS works without it
   • Agree: clocks can't detect it
   • Disagree: GPS depends on it
4. 4.

   Luz says a muon would notice its own life stretched. Agree or disagree?

   • Disagree: it lives 2.197 μs in its frame
   • Agree: it feels 10 times longer
   • Agree: it feels its time stop completely

5. 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

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 0.1 km
   • About 116.0 km
   • About 11.6 km
7. 6.

   Using the table, how are GPS satellite clocks set before launch, Noah?

   • Slightly fast, to add to the effect
   • Slightly slow on the ground
   • They aren't adjusted at any point
8. 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
9. 8.

   At 0.1c, γ is about 1.005. What does this say about everyday speeds, Ren?

   • Time dilation is tiny at them
   • Clocks run at half speed
   • Lengths double at them
10. 9.

    At about what speed is γ equal to 2, Tala?

    • About 0.87c
    • Twice c, 2c
    • Half of c, 0.5c
11. 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