It’s been a while since I posted anything in the Cute Problems category, so since Spring is in the air I thought I’d post a physics problem which involves springing into the air…
Two identical fleas, each of which has mass m, sit at opposite ends of a straight uniform rigid hair of mass M, which is lying flat and at rest on a smooth frictionless table. If the two fleas make simultaneous jumps with the same speed and angle of take-off relative to the hair as they view it, under what circumstances can they change ends in one jump without colliding in mid air?
UPDATE Monday 10th March: No complete answers yet, so let’s try this slightly easier version:
Two identical fleas, each of which has mass m, sit at opposite ends of a straight uniform rigid hair of mass M, which is lying flat and at rest on a smooth frictionless table. Show that, by making simultaneous jumps with the same speed and angle of take-off relative to the hair as they view it, the two fleas can change ends without colliding in mid-air as long as 6m>M.
Answers via the comments box please..
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