Newton's First Law: "Every object persists in its state of rest or uniform motion in a straight line unless it is compelled to change that state by forces impressed upon it."
Newton's Second Law: Force = Mass x Acceleration or, Force = change of momentum x change of time.
Newton's Third Law: For every action there is an equal and opposite reaction.
How These Laws Apply To Our Ballista
Newton's First Law: Our water balloon will travel at an unaltered rate if unaffected by gravity. Our balloon is affected by gravity so it will arc.
Newton's Second Law: If we measure the mass of our water balloon, then calculate the force of the water balloon after leaving the ballista we then calculate the acceleration of our water balloon.
Newton's Third Law: As the tension from the rope on the ballista increases the force of its release will be that much greater.