Trouble figuring out a Catapult simulation

Game Mechanics
#1

I want to make a game similar to this one and cant figure out how to move the “tomato”

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I know that i can get Y from the position of the yellow line in the middle.
What i cant figure out is how to set when the “tomato” will hit the ground.

Some help please?

#2

2D projectile arc + matrix calculation.

Calculate how an object moves when you it at an angle facing X axis, on a 2D Cartesian plane.

Then use 3D matrix calculation to rotate the arc by its yaw, to the direction of the vector going through the screen.