A ball is thrown straight up at 15m/s. How long does the ball take to reach apex? What is the ball's total time of flight? ... ?

We use one fundamental kinematic equation for this problem. It is expressed as:

v^2 = v0^2 - 2gh

For this case, v = 0 and v0 = 15

h = v0^2 / 2g = 15 / 2 (9.8) = 0.77 m

Then, we use the equation:

h = (v0) t-g t^2 / 2

0.77 = 15t - (9.8) t^2 / 2

t = 0.05 s