A suitable algorithm for estimating the height(z) of a flying object?

I'm trying to figure out the height of a flying object, like the tennis ball in the picture below. Currently, I'm not using a stereo camera, and I'd like to tackle this problem only with a monocular camera. Any help will be appreciated!

Strictly speaking, you can't because the ball could be anywhere along the ray to the observer. To some extent you can use the apparent ball diameter to estimate the distance to the observer, but this will be pretty inaccurate. If the ball is measured close to the player, you'd better rely on the player's anatomy.

Another option is to determine the location of the feet of the player, as you known that they rest on the ground plane, and you can use the white lines as a reference. Then you can admit that the ball is at the vertical of a foot.

In any case, you need to be familiar with projective geometry and calibration techniques.

Yet another option is to use a camera that is far away and pointing horizontally (ideally with a telecentric lens, but this is not affordable). In this case, all points of equal height appear approximately on the same horizontal on the image.