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
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.