A ball is thrown directly downward with an initial speed of 8.00 m/s, from a height of 30.0 m. After what time interval does it strike the ground?

We can use the equation of motion:

s = ut + 1/2 x at²

Both the velocity and acceleration are downwards so we'll consider the downward direction positive

30 = 8t + 4.91t²

4.91t² + 8t - 30 = 0

Solving the quadratic:

t = 1.79 s; t = - 3.42 s

Negative time is not possible so second value discarded. Time taken = 1.79 seconds