An object moving due to gravity can be described by the motion equation $y=y_0+v_{0}t-\frac{1}{2}g{t}^2,$ where $t$ is time, $y$ is the height at that time, $y_0$ is the initial height $($at $t=0),v_0$ is the initial velocity, and $g=9\mathrm{.}8\frac{m}{s^2}($the acceleration due to gravity$).$

If you stand at the edge of a cliff that is $75$ m high and throw a rock directly up into the air with a velocity of $20\frac{m}{s},$ at what time will the rock hit the ground? $($Note: The Quadratic Formula will givedt two answers, but only one of them is reasonable.$)$

Express your answer in seconds.