Answer
The height of the slide should be 1.0 meter
Work Step by Step
We can use conservation of energy to solve this question. The potential energy at height $h$ will be equal to the kinetic energy at the bottom of the slide. Therefore;
$PE = KE$
$mgh = \frac{1}{2}mv^2$
$h = \frac{v^2}{2g}$
$h = \frac{(4.5~m/s)^2}{(2)(9.80~m/s^2)}$
$h = 1.0~m$
The height of the slide should be 1.0 meter.
