Three Questions

Week one in physics, we probably discussed the following question for about 20 minutes:

If a physics textbook is dropped from a certain height, and an identical textbook is thrown straight down and released from that same height, which book will have gained more speed while in the air? (Air resistance ignored).

Then, earlier this week we discussed the following question:

Starting from rest, a ball can either roll down a steep ramp or a shallow ramp that both start at the same height above the ground. Which ramp should you send the ball down so that it gains the most speed by the time it gets to the bottom?

Then today, we probably spent about 20 minutes discussing this question:

If a physics textbook is dropped from a certain height, and an identical textbook is thrown straight down and released from that same height, which book will have gained more kinetic energy? (Air resistance ignored).

Each question alone is perplexing and interesting in its own way, but the real perplexity lies in the collection of answers and arguments among them.