When Pal throws his beach ball straight up in the air, it's height h at time tis given by h=(-1/2)gt^2+v(sub 0). Find the velocity of the ball at time t.

Your equation in not correct.

h=(-1/2)gt^2+v(sub 0)*t

The velocity at time t is the derivative

v(t) = v*sub0 - gt