Answer
$ 0.72m$ or $72cm$
Work Step by Step
lets first compute how much time he takes to complete his jump. let $v$ be his initial velocity which can be given as
$ v = \sqrt{2gh}$
$ v=\sqrt{2*10* 0.55} ms^{-1} $
$ v=\sqrt{11}ms^{-1 } = 3.3ms^{-1}$
time taken to complete his jump is
$ t= \frac{0.55m}{ 3.3ms^{-1}}$
$t= 0.17s$
now when he jumps in elevator the elevator will desend some distance which is
$s = vt = (1.0* 0.17 )m =0.17m$
thus his total jump will be
$0.55m +0.17m = 0.72m = 72cm$
