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Physics/Projectile Range


QUESTION: If two balls of identical size are launched with the same initial velocity at some angle greater than horizontal, which will fly farther, and why?

My 9 year old daughter and I are getting ready for a science fair, and we launched a great deal of balls at various angles and ball densities, so I know what the experimental answer is (the denser balls fly farther downrange), but I need to be able to teach/explain it to her, and I'm afraid I can't find a good source that explains it well.

ANSWER: It's all a balance between time in the air and horizontal velocity.  So for projectiles you need to maximize horizontal velocity (minimize angle), but you want to balance that against vertical flight time.  So if your balls are launched with the same energy, the higher-mass (more dense) balls will travel slower and not fly as far.  If your balls are too fluffy, air drag becomes a consideration.  If you're looking for more specifics, please add a few details about what you'd like to try (i.e. how you launched the balls) and I can be more specific about what's affecting your launch distances.

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QUESTION: The launch energy was not the same, but the launch velocity was. Surface fluffiness was also the same.  Only the ball density varied.

ANSWER: OK, that doesn't tell me how you launched the balls.  How do you know that the energy was different, but the velocity was the same?

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QUESTION: The cradle that held the balls was very massive compared to the mass of the balls, and there was a good deal of friction (by comparison) associated with the launch.  The assumption was that almost all the energy in the rubber bands was used up in the operation of the catapult, so the slight variance in (catapult+ball) mass wouldn't change the launch velocity by any significant amount.  Of course the energy imparted to the balls was different in proportion to the mass of the balls.

The device was a heavy wooden cradle sliding up a wooden plane and pulled by stretched rubber bands. The balls were either wooden or smooth styrofoam, and 1" diameter +- .01".

I figured out the answer already, but thought your explanation might help others.  My daughter found this fascinating, as do I.

Thanks for doing what you do.

Ahh, so the balls would have been going with very similar velocity when launched in a heavy cradle, yes.  The larger one would go slightly slower, of course, but from your description it probably wouldn't be much.  So in that case, the air resistance (a complex phenomenon, partly friction and partly the energy of moving the air out of the way as the ball passes through) would be your dominant factor.  That, of course, would cause a lighter ball to lose energy and velocity faster than a heavier ball.

Good luck with the science fair.


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Dr. Stephen O. Nelson


I can answer most basic physics questions, physics questions about science fiction and everyday observations of physics, etc. I'm also usually good for science fair advice (I'm the regional science fair director). I do not answer homework problems. I will occasionally point out where a homework solution went wrong, though. I'm usually good at explaining odd observations that seem counterintuitive, energy science, nuclear physics, nuclear astrophysics, and alternative theories of physics are my specialties.


I was a physics professor at the University of Texas of the Permian Basin, research in nuclear technology and nuclear astrophysics. My travelling science show saw over 20,000 students of all ages. I taught physics, nuclear chemistry, radiation safety, vacuum technology, and answer tons of questions as I tour schools encouraging students to consider careers in science. I moved on to a non-academic job with more research just recently.

Ph. D. from Duke University in physics, research in nuclear astrophysics reactions, gamma-ray astronomy technology, and advanced nuclear reactors.

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