Question

a ball is thrown directly downward an with initial speed of 8.00 m/s, from a heightnof30.0 m. After what time interval does the ball strike the ground?

Answer 1

\[\Delta y = \frac{ 1 }{ 2 } a t^2+v _{i}t \]
\[0 = \frac{ 1 }{ 2 } a t^2+v _{i}t + \Delta y\]
\[0 = \frac{ 1 }{ 2 } g t^2+v _{i}t + \Delta y\]

Above is a general kinematics equation for you. I manipulated it so it's more in line with your problem. All that's left to do is plug in and solve for t!