This question is about time dilation and relativistic mass.
Muons are produced in the upper atmosphere of Earth and travel towards the surface of Earth where they are detected. Explain how, with reference to the situation described in (b), the production and detection of muons provide evidence for time dilation.
the muons are equivalent to S and the Earth to X, Y;
without time dilation most muons would decay before reaching the Earth's surface;
from the Earth frame, with time dilation, the (proper) half-life of muons becomes dilated/larger;
from the muon frame, with time dilation, the (proper) journey time is less than that on Earth;
fewer muons decay/more muons survive than expected without time dilation.