The equation for a projectile's height versus time is. A tennis ball machine serves a ball vertically into the air from a height of two feet, with an initial speed of 120 feet per second. After how many seconds does the ball attain its maximum height?

The time it takes the ball to reach its maximum height only depends on

its initial vertical speed. The height from which it's launched makes no

difference.

Since you're still reporting height in 'feet' and speed in 'feet per second',

we can assume that you haven't achieved space travel yet, and this whole

episode with the tennis ball is taking place on Earth. So we know that the

acceleration of gravity is 32.2 ft/s², and the ball will lose 32.2 ft/s of its

upward speed every second. Naturally, it'll stop rising when its vertical

speed has shriveled to zero.

That happens in (120/32.2) = 3.73 seconds after the launch.