I’m watching Season 2 of “The Simpsons” and in “Bart vs Thanksgiving”, Bart throws a football and then catches the ball.
Now clearly, if I throw a ball straight up, it will come back down and I can catch it.
If I throw it a few feet from my current position, I can clearly still catch it.
So my question is, how far can I throw a ball from my current position and reasonably expect to catch it? Feel free to assume I’m Batman* and use maximum human potential.
Which way is the wind blowing, and how fast?
How fast can you run?
Uphill, level or downhill?
Can you and the ball both be in freefall?
Do you throw like a girl?
What’s the size of the ball, relative to your own size?
Is it a balloon or a bowling ball?
Can you catch with your feet?
Are you a centipede?
Are you under water?
Are you in space?
Why don’t we assume that this question is based on a hypothetical human who is capable of matching any world record holder for sprinting or running and any world record holder for throwing, say, a softball.
The whole thing takes place on Earth, at STP.
The problem is that throwing for maximum distance is not necessarily the same as throwing for maximum flight time.
So the world record for throwing a cricket ball (I don’t play baseball, but the balls have a similar regulation size and weight) is 132 meters.
Plugged into a ballistic trajectory calculator, that gives a maximum initial velocity of 36 m/s (at 45[sup]o[/sup] launch angle), and a flight time of 5.1 seconds.
No man alive can run 132 meters in 5.1 seconds.
At an angle of 90[sup]o[/sup], the flight time is 7.3 seconds.
At 75[sup]o[/sup], the flight time is still 7 seconds, and the ball travels 66m.
Usain Bolt could probably manage that, but hardly anyone else.
An 80[sup]o[/sup] throw goes 45 meters, and takes 7.2 seconds - that might be easier.
So the answer is probably somewhere in the range of 40-70 meters.
The OP said “football” not baseball. The world record throw for a rugby ball is 163.32 feet (just short of 50 metres. Hard to tell from the video but the ball looks to be in the air for less than ten seconds, so even an average runner could manage that.
Related xkcd What If?:
How high can a human throw something?
Bottom line was a golf ball, about 260 feet.
si_blakely, the math to find the optimal angle is actually fairly simple. First, get the maximum possible throw speed and the maximum possible human running rate. Divide the running rate by the throw speed, and then take the inverse cosine, and that’s the angle you want.
From there, there are a number of methods you can use to find the range, but the simplest is probably R = v^2*sin(2θ)/g
Real world the key is going to be how optimally slow a person needs to throw a ball to be able to heave it, then recover and begin running and wind up in position X to catch it. To keep a ball in the air along a relatively flat trajectory curve requires a good bit more speed than any person can run so it’s going to need to be a high curve of some kind so the person can catch up to it.
Lets say Usain Bolt throws the ball
http://io9.gizmodo.com/the-physics-of-usain-bolts-world-record-100-meter-dash-924744818
Limits of speed[edit]
So let’s say he throws the ball and throwing then recovering a running stance and taking off takes one second. Knowing his ground speed the question is then how much energy can he put into the ball to keep it in flight . Let’s say Vinny Testaverde’s 80 yard throw is close to max human potential.
https://www.reference.com/sports-active-lifestyle/longest-football-throw-history-6b2b4c821b672b5c
So let’s say a human being can run as fast as Bolt and throw as far as Testaverde and you account for the second recovery time after the throw. What is the curve required for maximum flight time that is still reachable at second delay adjusted running speed.
The world record for a frisbee is 308 feet.
I don’t know. AAAAAAAAAAAaaaaaaaaaaaaaaaaa…
(might be too obscure)
Thanks for the answers everybody. It looks like about 40-50 meters. That’s actually a lot further than I would have thought. I need to go search YouTube to see if there’s any video of somebody catching their own (somewhat) long ball.
Gone viral: High school football phenom Gary Haynes catches his own passes - YouTube <----- 40 yards but I’m going to see if I can find something even longer.
I’d be curious to see how far RGIII could do it(or maybe could have done it before his injuries) Best combination of great speed and strong arm I can think of.
Michael Vick, IIRC, was faster and had a stronger arm, at his peak.
I kinda forgot about him, but I’d still rather see RGIII do it cause I like him more 
That doesn’t seem right to me. On long passes in the NFL, which at their longest are about 40-50 metres, the receiver often has to be running full tilt to receive the ball at the point where it comes down. Obviously, the receiver already has a pretty big head start.
The NFL standard for hang time is considered to be a tenth of a second per yard, which is equal to a pretty fast runner on the ground. So a 50 yard punt should be in the air for five seconds, and a good runner can run 50 yards in five seconds. That distance is doable. A ball in the air over 50 yards, drops off that linear relationship, so that would be about the maximum attainable. An NFL average of 40-yard punt is 50 yards in the air, and measured from the line of scrimmage, and hang time of 6 seconds is unattainable. So it’s really four seconds hang time for a ball flying 50 yards.
A thrown football, once it is in the air, acts exactly the same as a punted one, so a strong passer can throw a ball 50 yards in the air, and run 40 yards in the hang time it comes down. which looks like the outer limit. A ball thrown farther than that will go well over a yard per ten seconds.
A runner cannot run 50 yards in five seconds from a standing start in the posture of just having made a long throw, and looking behind him in the air to judge where the ball will come down to be caught, which would add a great deal of difficulty to meeting the optimum long throw and running speed. The punt strives for a sweet spot of distance/hang time, so a thrown ball would have to be thrown more vertically, to gain hang time at the expense of distance, thus reducing the distance to maybe only 30 yards, and in an actual competition, I’d expect skilled and practiced players to be in that range. I would doubt if anybody could come anywehre near 40 meters. A kid like Bart Simpson would not be among the finalist, and would probably fail to make even ten yards.
Don’t punts have much higher arcs than thrown passes and therefore a longer hangtime per distance traveled?
Not on this board.
You misspelled yards.
Living overseas, I think in meters as well, except for golf and football.
I’m thinking it’s going to be way less than that given the very steep curve needed to keep a ball airborne and catchable and the recovery time to run needed.
Yes, but the strategy of throwing a pass to yourself would use a punt-like trajectory in order to maximize hang time for distance thrown. The OP’s question does not imply a bullet pass, for which the answer would obviously be zero.
When we were kids playing two-man touch football, we employed a rule that you could pass to yourself, and you were not downed by being touched while the ball was in the air. But they were mostly underhand tosses of only a few yards. Even then, five yards was easy, and ten probably attainable with just a soft toss, with sufficient practice.
In basketball, on a fast break, a player can beat a thrown ball half the length of the court.