$1.$ A child, initially at rest at the top of $3\mathrm{.}55$ m high slide, slides down to a height of $0\mathrm{.}480$ m$.$ At the bottom of the slide, the child has a speed of $2\mathrm{.}45$ m$/$s$.$ If the mass of the child is $34\mathrm{.}5$ kg$,$ what is the change in mechanical energy of the child?

$\mathrm{}\mathrm{}2.$ If a $70\mathrm{.}0$ kg student runs up a flight of stairs $15\mathrm{.}0$ m high in $25\mathrm{.}0$ s$,$ what is the average power?

$\mathrm{}\mathrm{}3.$ A $65\mathrm{.}0$ kg student climbs a set of stairs in $25\mathrm{.}0$ s with a power output of $95$ W$.$ What is the vertical height of the stairs?