Data we have:
m: mass; m = 0.5kg
g: gravitational acceleration; g = -9.81m/s^2 (negative since this acceleration is downward)
vi: initial velocity; vi = 36m/s (positive since this velocity is upward)
vf: final velocity (velocity at the top); vf = 0m/s
We need to solve for d: distance it travels, so let's use this formula:
vf^2 = vi^2 + 2gd
Let's plug in the variables we know:
0^2 = 36^2 + 2*(-9.81)*d
Solve for d:
Move 36^2 to the other side, then negate both sides to remove the negative sign from both sides:
36^2 = 2*9.81*d
Divide by (2*9.81) to isolate d:
d = 36^2/(2*9.81)
Finally, solve:
d = 66.1 m