Answer
The high jumper needs to be able to sprint at a speed of $4.85~m/s$
Work Step by Step
We can assume that all the kinetic energy will be converted into gravitational potential energy:
$\frac{1}{2}mv^2 = mgh$
$v^2 = 2gh$
$v = \sqrt{2gh}$
$v = \sqrt{(2)(9.80~m/s^2)(1.2~m)}$
$v = 4.85~m/s$
The high jumper needs to be able to sprint at a speed of $4.85~m/s$
