A basketball and a volleyball can reach the same height and travel the same distance when thrown. Pretty well anything can reach the same height and travel the same distance, but maybe you mean to ask what will travel further if you through them with the same force. In this explanation, I will provide a term followed by a letter representing that term. For example, I'll write "force F" in a sentence so that when I write an equation with "F" in it you'll know that stands for force.

Say you apply the same amount of force to a basketball as you do to a volleyball for the same amount of time. Which one goes farther? The answer depends on how heavy the basketball and volleyball are, or how much mass they have. A man named Isaac Newton figured out this physical law. He called it his second law of motion.

Newton's second law of motion states that the force F acting on an object will equal its change in momentum Δp with respect to time Δt (F = Δp / Δt, where / means divided by).

Newton defined momentum p as the mass m of an object multiplied by its velocity v (p = m * v).

Since the mass of an object doesn't usually change, the change in momentum is usually equal to the mass times the change in velocity Δv ( Δp = m *Δv). Since Newton's second law says that F = Δp /Δt, we can also write it as F = m * Δv / Δt.

If we solve the equation for Newton's second law F = m * Δv / Δt for the change in velocity, we find that Δv = F * Δt / m. What this equation means is for a fixed force and change in time, the change in velocity will be greater for a smaller mass than a bigger mass. If we divide one quantity by a smaller number we get a bigger number back than if we divide by a bigger number.

According to Newton's second law, if we apply the same force to both the lighter volleyball and the heavier basketball for the same amount of time, the volleyball will have a bigger change in velocity. Since the basketball and volleyball are not moving to begin with, this bigger change in velocity means that the volleyball will be traveling faster than the basketball.

If we don't think about air resistance, the volleyball's larger velocity will result in it traveling further than the basketball. If we do think about air resistance, things get much trickier because air resistance gets bigger with velocity. With our analysis, however, it's safe to say that the volleyball will travel farther if we throw it as hard as the basketball.

Keep questioning,

I believe what makes the difference in this is gravity and density. We have to think about how air resistance affects certain objects, so maybe what might help is if we can think about which object would fall down faster due to gravity and whichever object were able to hit the ground faster, would probably be able to be thrown farther. So basically, think of our arm strength throwing the ball is gravity, and think of the ground as like a "max distance." If you recall, there is an experiment where if you put two items: a feather and a rock inside of a vacuum so that there is no air, they both fall at the same speed. What matters is not the weight, but the density and a more dense object will be able to "go father".

But if you were to throw it, what makes it complicated is that, it will take more energy to accelerate the more massive object and you find that: a light mass will accelerate quickly, but then slow down due to the air, while a massive object will not move at all (it will not start as fast, but it will not slow down because of air). And you must also remember that things with more mass will have more inertia...so I believe if you use the equation F=ma where f = force in newtons, m = mass in kg, and a is acceleration (m/s²). You may be able to find out!