If an object is dropped from an initial height $h,$ its velocity at impact with the ground is given by

$v=\sqrt[\phantom{2}]{2gh}$

where $g$ is the acceleration due to gravity and $h$ is the initial height.

$($a$)$ Find the initial height $($in feet$)$ of an object if its velocity at impact is $53f\frac{t}{sec}.($Assume that the acceleration due to gravity is $g=32f\frac{t}{se{c}^2}.)$ Round to the nearest hundredth of a foot, if necessary.

$($b$)$ Find the initial height $($in meters$)$ of an object if its velocity at impact is $34\frac{m}{sec}.($Assume that the acceleration due to gravity is $g=9\mathrm{.}8\frac{m}{se{c}^2}.)$ Round to the nearest tenth of a meter.