Here's a first-order approximation. I'll assume the angle is perfect and work out the speed range. The first ball decelerated to maybe 8 m/s given its altitude at collision and some loss to air friction. If the ball is 25 cm wide, it crosses its own diameter in 1/32 second.
Assume the distance of the collision is 10m from launch and occurs 1.7 seconds after the second kick. The margin of error on the arrival time is 1/32 / 1.7 = 1.84%. Using your launch speed centered around your value of 38 mph = 16.9875 m/s, that means the possible range was 16.675 to 17.300 m/s. Interestingly, that's a difference of 1.4 miles per hour, which is also roughly the precision of velocity that baseball pitchers can produce on demand.
By the way, there's more variables on the inputs to the second ball. The timing of the kick is important and controllable too, creating a three-dimensional map of inputs. This could be transformed into and visualized as a 3D graph, showing all the combinations of speed/angle/timing that will result in a collision.
Also, the left-to-right angle must be on target too or the balls won't be in the same vertical plane for any collision at all.
About the vertical angle that you assumed to be perfect: I don't think that is critical. If you hit the second ball a bit higher/lower than intended, it crosses the trajectory of the first ball higher/lower than intended, so it must be at the intersection point earlier/later. Luckily, you get some of that for free, as the intersection point will be closer by/farther away.
All else being equal, the harder you can kick, the easier this gets. The lower the arc of the first ball, the smaller the angle of intersection between the two trajectories, and the easier the hit. You can get a lower arc by giving the ball more horizontal speed, keeping vertical speed the same (just decreasing vertical speed won't help; the first ball would hit the floor before you can hit it with the second ball)
Of course, all else isnt equal; directional errors likely are some function increasing with both distance and ball speed.
Assume the distance of the collision is 10m from launch and occurs 1.7 seconds after the second kick. The margin of error on the arrival time is 1/32 / 1.7 = 1.84%. Using your launch speed centered around your value of 38 mph = 16.9875 m/s, that means the possible range was 16.675 to 17.300 m/s. Interestingly, that's a difference of 1.4 miles per hour, which is also roughly the precision of velocity that baseball pitchers can produce on demand.
By the way, there's more variables on the inputs to the second ball. The timing of the kick is important and controllable too, creating a three-dimensional map of inputs. This could be transformed into and visualized as a 3D graph, showing all the combinations of speed/angle/timing that will result in a collision.
Also, the left-to-right angle must be on target too or the balls won't be in the same vertical plane for any collision at all.