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A Fun Free-fall Puzzle

September 15, 2011

One puzzle I have enjoyed thinking about despite its “school-science” feel is this one:

Three identical balls are thrown three different ways from the 3rd story balcony of a building. Air resistance is negligible.

The first ball is thrown vertically upward

The second ball is dropped

The third toss is thrown vertically downward with same speed as the first ball

For each ball, consider only the stretch of time between when that ball leaves the hand and just before it hits the ground:

Part 1: Rank the change in speed

Part 2: Rank the change in velocity

Part 3: Rank the change in kinetic energy

If you are really looking to test some students on their understanding of the difference between speed, velocity, and kinetic energy, this one should do the trick.

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One Comment leave one →
  1. September 16, 2011 12:33 pm

    Spoiler alert:

    “Change in speed” : II > I = III

    “Change in velocity”: I > II > III

    “Change in KE” : I = II = III

    Any disagreements or dissent out there? I think the most interesting thing to think through is how change in speed and change in KE could be different. I don’t mean just proving that they are different, but finding the flaw in thinking that they should be the same. It’s terribly reasonable to think they should be the same ranking because KE and speed have a clear monotonic relationship. For example, here’s the thinking: “Change in KE is all the same, and we know that KE = 1/2 mv^2. So the change in speed must be the same as well.”

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