In light of the recent tricky class problem (falling object spends 1 s to fall the seconcnd half of its motion), I submit a couple of other fun ones for you to try:
1. A juggler can toss a ball a certain height H. To what height must the ball be tossed to spend twice as much time in the air?
2. If you drop a ball on the Moon (where g is 1/6 that of Earth), how does the time to fall compare to the time of fall for the same object on the Earth? How would the answer be different on Jupiter (where g is around 2.3 times that of Earth)?
3. Drowsy cat problem. Imagine a drowsy cat sitting in a window (2-m tall). The cat sees a ball fly up the window, past the top sill, and back down. The ball is in view for a total of 0.5 seconds. How high above the top of the window sill does the ball go? (Answer: 2.34 m. This is a tricky problem.)
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