Is it possible for Cav to hit Cat in 1 turn?

Is it possible for a cav to hit a cat in 1 turn without the cat hitting back? such at 145 speed and max lvl marching?

No

Well... If they have low shooting skill yes. Field length will be shorter.

An archer can tho ^__^

if they have level 0 shooting and your speed is maxed with equipment and lvl 10 marching speed its possible o_0

It is possible on two conditions....

—the cats have shooting tech level 1 or 0 = 816/800
—the cav are max speed = 825

The field length at most will be 1116...(300+highest range)
for our experiment we'll say tue cats are also max speed = 137

The cats must advance three times before they can reach the furthest end of the field.
Therefore, the cav must pause until the cats have moved twice, and on the third turn, advance to hit the cats.
They will suffer no casualties if there are enough to kill the cats outright.
If there are not enough cav, they will be counterattacked, but will likely win this scenario.

It is important to note.....

This scenario is in all rights a stalemate...when just cats are facing cav alone under these circumstances.
The cats should advance two turns and pause for a cav charge. Then they can hit one round and retreat on the next. If pursued, they can hit the cav without being hit, as cav can't hit a retreating cat. This will gain two extra attacks, which is all it should take to mop up the cav.
If you find yourself in this position, fool the cavs by entering an advance charge with the cats, and right before the timer runs out for round three, pause the cats instead, trapping his horses under a deadly rain of boulders and burning oil.

Hope this helps!

Edit: the cav don't really need max speed, just a fairly high one. For instance, if you've maxxed speed attribute and paired that with max equipment, you could have a marching tech level 0 and the scenario would play out the same. There's just too many combinations of speed to discuss, as long as the cav can move 705, the scenario will work.

Or your infantry speed is 5000 and still climbing