A spaceship moves away from Earth at a
speed 0.861 c and fires a shuttle craft that
then moves in a forward direction at 0.312 c
relative to the ship. The pilot of the shuttle
launches a probe forward at a speed 0.639 c
relative to the shuttle.
A)Determine the speed of the shuttle relative
to Earth. Answer in units of c.
B)Determine the speed of the probe relative to Earth. Answer in units of c.
speed 0.861 c and fires a shuttle craft that
then moves in a forward direction at 0.312 c
relative to the ship. The pilot of the shuttle
launches a probe forward at a speed 0.639 c
relative to the shuttle.
A)Determine the speed of the shuttle relative
to Earth. Answer in units of c.
B)Determine the speed of the probe relative to Earth. Answer in units of c.

Use the relativistic formula for addition of velocities.
The shuttle's velocity relative to Earth will be
v = (0.312 c + 0.861 c)/( 1 + 0.312 c * 0.861 c / c^2) = 0.925 c
The probe's velocity relative to Earth is
v = (0.925 c + 0.639 c)/( 1 + 0.639 c * 0.925 c / c^2) = 0.983 c
The shuttle's velocity relative to Earth will be
v = (0.312 c + 0.861 c)/( 1 + 0.312 c * 0.861 c / c^2) = 0.925 c
The probe's velocity relative to Earth is
v = (0.925 c + 0.639 c)/( 1 + 0.639 c * 0.925 c / c^2) = 0.983 c