Sensors to detect high speed object crossing plane
Do the math.

600 meters per second is 1342 miles/hour.  Mach 2.0 is 680 m/sec.  We're talking "bullet" here.

Assuming 5 mm for the projectile length, it will cross the plane in 8.33 microseconds.  A 20mm projectile will take all of 33.3 microseconds.

The traditional way to measure the accuracy and precision of a bullet trajectory is to shoot it at a piece of paper, and see where the hole shows up.

You COULD use something like black construction paper, lit from behind (light OFF AXIS!) and use a TV camera to detect the sudden appearance of a bright spot where there wasn't one, where the newly-punched bullet hole is now letting light through.  An Arduino is going to be kind of wimpy for image processing, though.