A Shower of Projectile Motion

I decided to take a break and shower after many hours of studying. Even though I tried to avoid thinking, a few physics concepts hit me on the head (quite literally actually). I realized that the stream of water coming out from the shower head exhibited projectile motion. Since the direction of the initial horizontal velocity was parallel to the ground and there was no initial vertical velocity, the equations in the picture represent the distance from the shower head to the ground and the horizontal distance from the shower head in which the stream of water lands. Since we learned in the projectile labs (the ones with the monkeys and bananas) that vertical and horizontal motion are independent, I know that when I adjusted the strength of the water stream, I was only changing the initial horizontal velocity (and therefore the horizontal displacement), not the time it takes for the stream of water to travel from the shower head to the ground. It's amazing how physics is everywhere in the world around us. We can never escape the laws of physics!