The speed of light and relativity

Answer Key - Grade 11 Science Worksheet

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

1. 1.

   A muon at rest lives 2.197 μs on average (PDG). Measured from the ground, how long does one moving at 0.99c last, to 0.01 μs, Ari?

   15.57 μs
2. 2.

   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?

   22 μs
3. 3.

   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?

   11.04 μs

4. 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. 4.

   Using the table, does a GPS satellite clock run fast or slow overall, compared with ground clocks, Jun?

   • Fast, by about 38.6 μs a day
   • The two effects cancel exactly
   • Slow, by about 38.6 μs a day
6. 5.

   Using the table, why does the satellite's height make its clock gain time, Luz?

   • Gravity is weaker up there
   • It is closer to the Sun
   • Its speed makes it run fast
7. 6.

   A rod moves past at 0.8c. Measured from the ground, how long is it along its motion, Milo?

   • Shorter than at rest
   • Longer than at rest
   • Exactly as long as at rest
8. 7.

   Muons made high in the air reach the ground in large numbers. Why, Noah?

   • They travel faster than light
   • Air makes them live longer
   • Their lifetimes are stretched
9. 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
10. 9.

    Can a particle accelerator push a proton to the speed of light, Tala?

    • Yes, at full power
    • No: close to c, but not to it
    • Yes, if its ring is big enough
11. 10.

    Sunlight takes about 499 seconds to reach Earth. What does this show, Zee?

    • Light's speed is finite
    • Sunlight slows down in space
    • Light arrives instantly