If a projectile fired beneath the water, straight up, breaks through the surface at a speed of 13m/s, to what height above the water will it ascend

Well if you had either the velocity or distance traveled i could tell you. But since you haven't all i can say for sure is that the water slowed the bullet down to 13m/s so lets say you knew the distance you would calculate how many meters it traveled and you would have your answer because in this situation, meters (height) = how many seconds spent going into the air.