Question

A football is kicked from a tee at 12 m/s at 72° above the horizontal. What is the maximum height of the football

Answer 1

The maximum height is reached when the vertical component of the velocity is zero.

vertical direction:
acceleration: a = -g = -9.81m/s²
velocity: v = -g*t + v₀
position: y = -0.5*g*t² + v₀*t + y₀

For v= 0:
0 = -g*t + v₀ => t = v₀/g 
Insert into position equation gives:
y(max) = (-0.5*v₀²/g) + (v₀²/g) + y₀ = (0.5*v₀²/g) + y₀