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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