Fred throws a rock from (x0,0) with a velocity u0 at an angle θ0 above the positive x-axis. Given x0, u0, θ0, t, calculate after a time t:
a. The position (x, y) and velocity (un, uf) of the rock relative to Frank. Apply the Lorentz transformations and calculate:
b. The time t', position (x', y') and velocity (ur, u') relative to Mary's frame.
c. Plug in x = 1m, u = 1000 m/s, θ = 45°, t = 10 sec, and v = c/2 to get values from both coordinate systems.