Everyday I'm jugglin'

A juggler is juggling with four balls. He tosses and catches two at a time so that the interval between the two tosses is maximal and constant, \(t = 0.4~\mbox{s}\). Each ball is tossed with the same initial velocity, so that it makes a parabolic path to his other hand. The distance between his hands is \(d = 50~\mbox{cm}\) and they are at a same height. What should be the initial speed of the balls in m/s so that they can reach up to \(h=78.4~\mbox{cm}\) in height?

Details and assumptions

  • Assume the juggler tosses the balls right after he catches them.
  • There are no other forces but gravity that act on the balls.
  • Acceleration due to gravity is \(-9.8~\mbox{m/s}^2\).

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