I think deriving the relativistic velocity correction formula (“formula”) sooner, or providing some additional background, might help with some confusion I have as described below.

My confusion is in regard to 2 moving objects approaching a “stationary” object from opposite directions, their associated frames of reference, and the “types of” velocities being observed. I am assuming that by “stationary” we mean an object has zero velocity relative to the velocity of light.

In module 3.8 exercise 1, we have 2 taxis approaching a “stationary” person from opposite directions, and the “stationary” person is observing the velocity (or rate) at which the gap between the taxis is closing. In this case we just add the 2 taxis velocities together even if the total is greater than the velocity of light. No confusion here (I hope!).

In module 5.4 exercise 2 and module 5.6 exercise 1, we again have two objects (taxis and spaceships respectively) approaching a “stationary” person from opposite directions. In this case, if we are observing the velocities of the moving objects relative to each other (not the velocity of the change in the gap between the moving objects), then the formula would be applied; the formula is applied with v and w being the velocities of the two moving objects relative to the velocity of light. If the velocity being observed is of one of the moving objects relative to the “stationary” person, then the formula can still applied but the velocity of the “stationary” person (v or w) would be zero.

I know it’s tough to be clear about this topic, but if any one has comments that would further clarify or confirm the above, that would be appreciated.