A.5 Galilean and special relativity questions for IB Physics

A cyclist travels north at $8.0{\text{m s}}^{-1}$ along a straight road. A car overtakes her, travelling north at $20{\text{m s}}^{-1}$. Both speeds are measured relative to the road. What is the velocity of the cyclist in the reference frame of the car?

A moving walkway at an airport carries passengers east at a constant $0.80{\text{m s}}^{-1}$ relative to the ground. Traveller T walks east along the walkway at $1.3{\text{m s}}^{-1}$ relative to the walkway. Traveller W walks west on the floor beside the walkway at $1.1{\text{m s}}^{-1}$ relative to the ground.

Frame S is fixed to a straight road. Frame S′ is fixed to a car moving at $15{\text{m s}}^{-1}$ in the positive $x$ direction. The origins of S and S′ coincide at $t=0$. At $t=20\text{ s}$ a pedestrian presses a crossing button at $x=200\text{ m}$. What is the $x^{\mathrm{\prime }}$ coordinate of this event?

A star in a binary system is 2300 ly from Earth. It moves in a circular orbit with an orbital speed of $140{\text{km s}}^{-1}$ and an orbital period of 8.0 days. The plane of the orbit contains the line of sight from Earth, so at one point in each orbit the star moves directly towards Earth and half an orbit later it moves directly away from Earth.

Three reference frames are:

I. a car travelling around a roundabout at constant speed
II. a spacecraft drifting in deep space with its engines off
III. a lift moving downwards at constant velocity relative to the ground.

Treat a frame fixed to the ground as inertial. Which are inertial reference frames?

Unstable particles called kaons have a half-life of 8.6 ns when measured at rest. In a laboratory, a beam of kaons travels at a speed of $0.92c$ along a straight evacuated tube.