Home > Uncategorized > Car Talk Projectile Motion Puzzle

Car Talk Projectile Motion Puzzle

If you aren’t familiar with the NPR radio show, Car Talk, you should check it out.

Anyway, this week’s show they shared the following puzzle.

Car Talk Puzzle: The Grasshopper Race

Essentially, this has two grasshoppers racing.  Each grasshopper can just  different a maximum distance (but they have to take multiple hops).  Can you solve this puzzle?  I am pretty sure you need projectile motion – but I am not sure that is a valid solution.

Just a warning, I will probably solve this puzzle and post it on my blog.  So, if you want a shot before I give the answer, be quick.

  1. Nicholas Adams
    February 14, 2012 at 7:28 pm

    I can think of two answers depending on which way the question is meant to be taken, are you interested in seeing our reasoning here before you post the answer?

    • rhettallain
      February 17, 2012 at 3:14 pm


      I would love to see what you think. Post your answers if you wish – it won’t stop me. But I agree with you that the question could be interpreted in different ways. Lets just see what Tom and Ray say tomorrow.

  2. Nicholas Adams
    February 17, 2012 at 9:42 pm

    I think the answer has to do with a few facts: 1), The grasshoppers are jumping and therefore only need to touch down on the track, not constantly touch each segment, 2) the small grasshopper’s jumps divide out perfectly to 144 inches whereas the large grasshopper’s doesn’t, and 3) the hypotenuse of a triangle is shorter than the two base sides. It all comes down to the bend in the course. What all this means is that the small grasshopper has to follow along the track perfectly (ie the ‘long’ way), whereas at 14 jumps the large grasshopper can cheat and jump across the area between the two sections of the track and gain a little time (ie the ‘short’ way). Since the x component of their vectors are the same and the race is decided on that x component, the big grasshopper wins because he basically exploits a loophole in the rules that allows him to get a little ahead. He never touches down outside the track, technically!

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