Describe what is meant by a frame of reference.

At a later time the police spacecraft is alongside Speedy’s spacecraft. The police spacecraft is overtaking Speedy’s spacecraft at a constant velocity.

Officer Sylvester is at a point midway between the flashing lamps, both of which he can see. At the instant when Officer Sylvester and Speedy are opposite each other, Speedy observes that the blue lamps flash simultaneously.

State and explain which lamp is observed to flash first by Officer Sylvester.

The police spacecraft is travelling at a constant speed of 0.5c relative to Speedy’s frame of reference. The light from a flash of one of the lamps travels across the police spacecraft and is reflected back to the light source. Officer Sylvester measures the time taken for
the light to return to the source as 1.2 × 10^–8s.

(i) Outline why the time interval measured by Officer Sylvester is a proper time interval.

(ii) Determine, as observed by Speedy, the time taken for the light to travel across the police spacecraft and back to its source.

a coordinate system / set of rulers / clocks;
in which measurements of distance/position and time can be made;

light travels at same speed for both observers;
during transit time Officer Sylvester moves towards point of emission at front/away from point of emission at back;
light from front arrives first as distance is less / light from back arrives later as distance is more;
Officer Sylvester observes the front lamp flashes first;

Award [0] for a bald correct answer without correct explanation

(i) the two events occur at the same place (in the same frame of reference) / shortest measured time;

(ii) \(y = \left( {\frac{1}{{\sqrt {1 - \frac{{{v^2}}}{{{c^2}}}} }} = } \right)1.15\);
Δt=1.15 x Δt₀;
1.48 x 10^-8(s);