Juggling Physics – Keeping a Ball in the Air

To get the latest opinions in the world of juggling I often visit and comment on rec.juggling group. Lots of interesting characters there. Anyway, someone suggested that it was possible to throw a ball in the air from a flat surface and keep it suspended for over 9 seconds.

This sounded a bit high so a little calculating was in order. These are just the kinds of problems that are sufficiently amusing. My initial figuring was that the longest a person could keep a thrown ball suspended in the air was 4.7 seconds and it could reach a height of 64 meters.

Derivation of the juggling physics figures

Assumptions:
Velocity up = 100 miles/hr (The best arms in the world can throw a baseball )
Translates to ~44 meters / second
Force pulling it down = 9.8 m/s/s (gravity)

Calculations
(Time in seconds, Height)
1 s, 39 m
2 s, 63.5 m
3 s, 63.4 m
4 s, 29 m
5 s, hits the ground

Since the fastest I could throw a baseball is about 60 mph, it figures 28 m is the maximum height for me.

Juggling physics experiment

To see if these numbers were even close to accurate, an experiment was in order.

Materials:
1. One golf ball – (lighter than a baseball so it may go higher.
2. Stop watch
3. A supportive sister
4. A wide open area of land

Procedure:
1. Throw ball up in the air as hard as possible.
2. Have sister start and stop timer
3. Record time in the air
4. Repeat procedure a total of 10 times.

Data:
Trials and time (seconds)
1. 4.01
2. 4.20
3. 4.96
4. 4.10
5. 3.96
6. 4.31
7. 4.05
8. 4.46
9. 3.85
10. 4.28

Calculations:
Average time = 4.22 seconds.

Discussion:
My predicted time was pretty close to the actual average time: 4.22 s versus 4.5 s. One source of error was fatigue. After the 3rd throw I was already tiring. The calculations do not account for this.

The predicted height was also pretty close. 21.8 m versus 28 m. Of course, this is only a calculated height as I didn’t really have a tape measure.

Incidentally, when my brother did a couple of throws he able to keep it in the air for over 5 seconds (5.4). That means my assertion that the most you could loft a ball was for 4.7 seconds is just wrong. I’m blaming this one on the fact that we were throwing golf balls instead of baseballs. That should skew the numbers higher.

Conclusions:
There is still no way you can throw 3 balls in the air and keep them up for 9 seconds.

My brother is a much better thrower than me.

Addendum:
And for some more Juggling Physics, check out these videos from a physics class at Rutgers. Or for the really mathematically minded, here are some juggling physics equations and explanations.

Now you’ve seen the experiment so how do you think you would do?  Try it out and let the rest of the joggling world know how long can you make a ball stay in the air?