Final answer:
The factors influencing the trajectory and characteristics of a vertical jet of water leaving a nozzle include the initial velocity, nozzle diameter, pressure, and force exerted. The velocity increases when water is forced through a smaller nozzle, and the height the water can rise depends on the pressure drop and velocity.
Step-by-step explanation:
The factors influencing the trajectory and characteristics of a vertical jet of water leaving a nozzle include the initial velocity of the water, the diameter of the nozzle, the pressure of the water, and the force exerted on the water. When the water is forced through a smaller nozzle, its velocity increases due to the conservation of energy. Additionally, the height the water can rise is influenced by the pressure drop and the velocity of the water as it leaves the nozzle.