Aball 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−gt^2 / 2
0.77 = 15t - (9.8)t^2 / 2
t = 0.05 s

Independent variable is something that is changed in a experiment.