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For an uniformly accelerated motion, we can write
where
is the acceleration of this motion, which in this problem is the gravitational acceleration, with a negative sign because it points downward, against the direction of the motion; h=0.540 m is the distance covered by the flea, and 
is the initial velocity.
At the maximum height, the velocity is zero, so
. Therefore we can solve to find :
where
At the maximum height, the velocity is zero, so