Topic 1.5: Galilean and special relativity (HL) Questions

State what is meant by proper time.

Calculate the Lorentz factor γ.

Two runners move along a straight track in the same direction at 7.0 m s⁻¹ and 4.5 m s⁻¹ relative to the ground. What is the speed of the faster runner as measured by the slower runner?

A jet flies at 250 m s⁻¹ relative to the ground and fires a flare forward at 40 m s⁻¹ relative to the jet. A second jet flies directly toward the first at 220 m s⁻¹ relative to the ground. What speed does the flare have relative to the second jet? (Take the first jet's direction as positive.)

Two events on a space-time diagram are separated by Δx = 3.0×10³ m and by ct = 5.0×10³ m. What is the space-time interval Δs between them?

A spaceship travelling at 0.70c relative to a star measures the speed of the star's light. According to special relativity, the measured speed is

For two events the time term satisfies (cΔt)² = 9.0×10⁶ m² and the space term (Δx)² = 4.0×10⁶ m². What can be concluded about the events?

A light pulse travels between two events on a space-time diagram. What is the space-time interval Δs between those two events?

A boat sails at 5.0 m s⁻¹ east relative to the water, and the water current flows at 2.0 m s⁻¹ west relative to the seabed. What is the boat's velocity relative to the seabed? (Take east as positive.)

A particle moves at 0.866c relative to a detector. Its Lorentz factor γ is closest to:

Why is the Galilean velocity transformation u' = u − v eventually replaced by special relativity?

A rod has a proper length of 50 m. It moves lengthwise past an observer at 0.60c (γ = 1.25). The length the observer measures is:

An aeroplane flies at 250 m s⁻¹ and is observed from the ground. Why are relativistic effects on its measured length and time negligible?

Which statement about reference frames is correct according to Galilean relativity?

Which of the following is a postulate of special relativity rather than a consequence of it?

A lamp at the centre of a fast-moving carriage flashes once. According to an observer standing on the platform, which wall of the carriage does the light reach first?

A walkway in an airport moves at 1.2 m s⁻¹ relative to the ground. A passenger walks along it at 1.8 m s⁻¹ relative to the walkway, in the same direction as it moves. (a) Determine the passenger's speed relative to the ground. (b) Determine the passenger's velocity relative to the ground if they instead walk the opposite way at 1.8 m s⁻¹ (take the walkway's direction as positive).

State the two postulates of Einstein's special theory of relativity.

A spacecraft passes a space station at a constant speed of v = 0.80c. (a) Determine the Lorentz factor γ for the spacecraft. (b) An astronaut on the spacecraft measures a proper time of 4.0 s for an experiment. Determine the duration of the experiment as measured by an observer on the station.

Explain why no worldline on a space-time diagram can make an angle greater than 45° with the ct axis.