Galilean & Special Relativity

9.A muon has a proper lifetime of 2.2 μs and travels at 0.98c relative to Earth. What is its dilated lifetime as measured from Earth?

10.The speed of light in a vacuum is the same for all inertial observers.

11.In Galilean relativity, which of the following is true about time?

12.Which of the following statements about the muon lifetime experiment are correct? (Select all that apply)

13.A spacecraft travels at 0.8c relative to Earth. It launches a probe forward at 0.9c relative to the spacecraft. What is the speed of the probe as measured from Earth?

14.Arrange the following steps to show that a muon can travel about 650 m in its lifetime.

15.Match each quantity with its correct description.

16.Arrange the following steps in the correct order to calculate the velocity of an object measured from a moving reference frame using Galilean velocity addition.

17.Which of the following statements about the Lorentz transformation equations are correct? (Select all that apply)

18.In Galilean relativity, how does the time interval between two events measured in one inertial frame compare with the time interval measured in another inertial frame moving at constant velocity relative to the first?

19.In Galilean relativity, the time coordinate of an event is the same in all inertial reference frames.

20.Which of the following are consequences of Einstein's postulates of special relativity? (Select all that apply)

21.Arrange the following steps in the correct order to derive the time dilation formula using a light clock.

22.A student on a train moving at constant velocity throws a ball straight up. To the student, the ball goes up and comes straight back down. To a person standing on the platform watching the train go by, the ball's path is:

23.A rocket of proper length 120 m passes Earth at 0.80c. What length is measured by an observer on Earth?

24.A clock moving relative to an observer ticks more slowly as measured by that observer than a clock at rest in the observer's frame.

25.Which of the following quantities are the same for all inertial observers? (Select all that apply)

26.In an inertial frame S, two events occur at the same place but 5.0 s apart. In a frame S' moving at 0.60c relative to S, the time interval between the events is:

27.Arrange these steps in the correct order to find the speed of a probe measured from the ground when it is fired forward from a rocket moving at 0.70c, with the probe at 0.50c relative to the rocket.

28.An event has coordinates x = 3 m and ct = 0 in frame S. In frame S' the event has x' = 3.5 m. What is the value of ct' in frame S'?

29.A muon is created in the upper atmosphere and travels towards the ground at 0.98c. In the muon's own rest frame, the distance from creation to the ground is measured as 2.0 km. What is the distance measured by an observer on the ground?

30.A light clock consists of two mirrors separated by a distance L, with a light pulse bouncing between them. An observer at rest relative to the clock measures the time for the light to travel from the top mirror to the bottom mirror. Which expression gives this time interval?

31.A light clock moves at speed v relative to a stationary observer. The light pulse must travel a longer diagonal path between the mirrors as seen by the stationary observer. Which quantity is unchanged by this?

32.A rocket of proper length 150 m moves at 0.91c relative to the ground. A probe is released from the back of the rocket at 0.45c relative to the rocket. How long does the probe take to reach the front of the rocket as measured by an observer at rest in the rocket?

33.A rocket of proper length 150 m moves at 0.91c relative to the ground. A probe is released from the back at 0.45c relative to the rocket. Which time interval does an observer on the ground measure for the probe to reach the front of the rocket?

34.A rocket moves to the right at 0.60c relative to the ground. A probe is released from the back of the rocket at 0.82c relative to the rocket (i.e. backwards). What is the speed of the probe relative to the ground?

35.An event P has coordinates x = 2 m and ct = 0 in frame S, and x' = 2.3 m in frame S'. Using the invariance of the space-time interval, what is the value of ct' in frame S'?

36.Which of the following are invariant quantities in all inertial reference frames? (Select all that apply)

37.A muon is created in the upper atmosphere and travels towards the ground at 0.98c. Which of the following statements are correct? (Select all that apply)

38.In a light clock, the time interval between ticks measured by an observer moving relative to the clock is longer than the interval measured by an observer at rest relative to the clock.

39.The space-time interval between two events is the same in all inertial reference frames.

40.Match each term with its correct description.

41.A spaceship travels at 0.8c relative to Earth. Calculate the time taken, as measured on Earth, to travel to a star 37 light-years away. Give your answer in years.

42.What term describes a quantity that is the same in all inertial reference frames?

43.Complete the sentence about the Lorentz factor.

44.Calculate the Lorentz factor γ for a speed of 0.8c. Give your answer to 2 decimal places.

45.Complete the statement of Einstein's first postulate.

46.A spacecraft moves at 0.6c relative to Earth. Calculate the Lorentz factor γ for this speed. Give your answer to 2 decimal places.

47.A spacecraft moves past Earth at 0.60c. A probe is fired forward from the spacecraft at 0.60c relative to the spacecraft. Calculate the speed of the probe as measured from Earth, giving your answer as a fraction of c to 2 decimal places.

48.What name is given to a quantity that has the same value in all inertial reference frames?

49.A train travels at 15 m s⁻¹ through a station. A child on the train runs in the same direction as the train at 2 m s⁻¹ relative to the train. Calculate the distance the child has moved after 10 s as measured by an observer on the platform. Give your answer in metres.

50.A travelator moves at 0.3 m s⁻¹ relative to the ground. A traveller walks along it at 1.5 m s⁻¹ relative to the travelator, in the same direction as its motion. Calculate the traveller's velocity as measured by a stationary observer on the ground. Give your answer in m s⁻¹.

51.A travelator moves at 0.3 m s⁻¹ relative to the ground. A traveller walks along it at 1.5 m s⁻¹ relative to the travelator, in the opposite direction to its motion. Calculate the traveller's velocity as measured by a stationary observer on the ground. Take the direction of the travelator as positive. Give your answer in m s⁻¹.

52.Plane A travels due north at 32 m s⁻¹ and Plane B travels due south at 45 m s⁻¹, both relative to the ground. Calculate the velocity of Plane A relative to Plane B. Take due north as positive and give your answer in m s⁻¹.

53.Explain the difference between Galilean relativity and special relativity.

54.State and explain one piece of experimental evidence that supports the theory of special relativity.

55.Explain how the muon lifetime experiment provides evidence for special relativity.

56.Explain why the muon lifetime experiment provides evidence for special relativity.

57.Explain how the muon lifetime experiment provides experimental evidence for special relativity.

58.A spaceship travels at 0.8c relative to Earth. Calculate the time taken, as measured on Earth, to travel to a star 37 light-years away. Give your answer in years.

59.Calculate the Lorentz factor γ for a speed of 0.8c. Give your answer to 2 decimal places.

60.A spacecraft moves at 0.6c relative to Earth. Calculate the Lorentz factor γ for this speed. Give your answer to 2 decimal places.

61.A spacecraft moves past Earth at 0.60c. A probe is fired forward from the spacecraft at 0.60c relative to the spacecraft. Calculate the speed of the probe as measured from Earth, giving your answer as a fraction of c to 2 decimal places.

62.A train travels at 15 m s⁻¹ through a station. A child on the train runs in the same direction as the train at 2 m s⁻¹ relative to the train. Calculate the distance the child has moved after 10 s as measured by an observer on the platform. Give your answer in metres.

63.A travelator moves at 0.3 m s⁻¹ relative to the ground. A traveller walks along it at 1.5 m s⁻¹ relative to the travelator, in the same direction as its motion. Calculate the traveller's velocity as measured by a stationary observer on the ground. Give your answer in m s⁻¹.

64.A travelator moves at 0.3 m s⁻¹ relative to the ground. A traveller walks along it at 1.5 m s⁻¹ relative to the travelator, in the opposite direction to its motion. Calculate the traveller's velocity as measured by a stationary observer on the ground. Take the direction of the travelator as positive. Give your answer in m s⁻¹.

65.Plane A travels due north at 32 m s⁻¹ and Plane B travels due south at 45 m s⁻¹, both relative to the ground. Calculate the velocity of Plane A relative to Plane B. Take due north as positive and give your answer in m s⁻¹.