Since the ball was launched at 45°above the horizontal, the 'x' and 'y' components of its initial velocity are equal, and each is
V₀ sin(45°) = V₀ cos(45°) = (1/2) V₀ √2 = 15.273 m/s .
The ball's horizontal speed is constant, so it reaches the goal posts in
(36 m) / (15.273 m/s) = 2.357 seconds.
The ball's vertical height above the ground at any time is
H = -16 t² + 15.273 t meters.
After 2.357 seconds, the ball is
-16 (2.357)² + 15.273 (2.357) meters off the ground
= -16 (5.555) + 15.273 (2.357)
= -88.88 + 35.998 meters off the ground.
This is not only well below the crossbar, it's also mathematically
below ground, down where da sun don't shan. This is algebra's
way of telling us that the ball returned to the ground before it ever
reached the goal post, and if it ever reached the goal post at all,
it was rolling in the grass when it got there.
