Dropped Clock Relativity Puzzle

Imagine that you’re standing on a platform hovering above a simple, non-spinning black hole. (You would need a rocket propelled platform to stay in place, of course, otherwise you’d fall straight in.) You have in your hands two synchronized, perfect clocks.

Now, drop one of the clocks off the edge of the platform to let it fall into the black hole.

Question 1: How fast is the dropped clock moving when it crosses the event horizon, relative to you back on the platform?

Question 2: When the dropped clock reaches the event horizon, how does the time it shows compare to the time you read on the clock in your hand?

Question 3: How does the time on the dropped clock compare to the one in your hand when the dropped clock reaches the center of the black hole?

Answers to come in a later post. (Or you can find out in chapter 7 of Crush.)