# Throwing a ball in my office

## Main Question or Discussion Point

First off, this is not a homework question. I'm 26, work in an office, have my BS in Finance and working on my masters in accounting to sit for the CPA. I am not a physics major.

In the office where I work, there is a wall from our section of cubes about 115-120 feet away. The ceiling is about 12 feet tall and some of them think they could throw a baseball from our cubes and hit the wall 120 feet away before it bounces without it hitting the ceiling. I don't think any of them could do it, and in order to figure out if it could be done we'd have to figure out what speed the ball would need to travel, etc. Does anyone know how I can work this out? Most of us are about 6 feet tall, so I'm sure we'd use 6 ft. as an exit point for the ball to travel from, but i'd need to change that variable for one of the guys who is a little shorter. I'm a logical person, so I'm sure I could figure it out if I knew what equation to use. I looked around the web for a bit to find random calculators, but I didn't really find one suitable for what I'm trying to figure out, so it looks like I'm going to dig a little deeper. :(

Thanks!

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If the ball reaches the top of its trajectory in the middle, you know it will have at most the time it takes to to fall from ceiling to floor to reach the other side. Calculate that time and you can know the horizontal velocity the throw would need. The total velocity will not be much more than that because of the shallow angle.

Would you know where to find time tables for a regular baseball falling 12 feet? I don't think the maintenance department would be too thrilled with letting me use their 10 ft. ladder to drop a baseball from the ceiling. Plus, I'm pretty sure my boss(es) would notice me lugging a ladder into the finance department. Everything I found online pointed to me knowing the time the ball is in the air. I have no way of measuring that, so i was hoping there would be another way.

If the height is Y, and you are on earth where the acceleration due to gravity, g, is 9.8m/s^2:

Y = 0.5*g*t^2

so the time, t is:

t = sqrt(2*Y/g)

which will be less than 1s. So you would need to throw faster than 60ft/s, or 40mph.

Janus
Staff Emeritus
Gold Member
It's a little more complicated than that since the person throwing the ball will not be releasing it from floor level. ( how high his release point would be depends on how he throws the ball.)

Let's say that with a sideways throw, he releases the ball at 4 ft above the floor. The time it takes for the ball to hit the ceiling will be the close to the time it takes for the ball to fall the 8 ft distance between ceiling and release point. this would work out to be about 0.707 sec. The ball will take 0.866 sec to fall from ceiling to floor, so the total time the ball could be in the air is 1.57 sec, for a speed of 76.4 ft/sec or 52 mph.

A higher release point will increase the required throwing speed. A release at 6 ft would require a throw of better than 55 mph.

Well it looks like others have beat me to doing the math.

I'd recommend using a denser ball if possible. That will make the approximations of the kinematic equations more accurate; basically it'll minimize air resistance.

sophiecentaur
Gold Member
Launching from the floor would be best, so could your rules include bouncing the ball off the floor first?
Is is nice to see that boyish behaviour is not dead! It has been almost eradicated in so many workplaces and I really appreciated it when I worked in a 'proper' job, several years ago.

berkeman
Mentor
Actually, it's even more complicated, but this point helps keep the ball from falling as much. With a baseball, the seams are used to minimize the drop of the ball when thrown over a medium or long distance (across the diamond, or from the outfield). Part of learning to throw a baseball is learning to always grip the ball with your fingers across a seam, and using that good purchase when you throw to flick your wrist down and give the ball a strong backspin.

A well-thrown baseball will almost look like it's travelling straight horizontally for a ways. It is falling, but slower than it would without the backspin holding it up.

So are you guys going to try it?

Hahaha. When the managers are away, we might. One of the other guys has a couple softball mitts in his car as a "safety". So, we'll see. :) Let's complicate matters a bit more. I agree that a 4 ft. launch point is doable, but what if we want it to hit the wall at least 4 feet from the bottom. I'm sure that changes things, but I don't know how to compute that.

berkeman
Mentor
I googled baseball trajectory +backspin, and got some great hits. Here's a page that has lots of "Physics of Baseball" links:

http://webusers.npl.illinois.edu/~a-nathan/pob/ [Broken]

Especially the part about The Effect of Spin on the Flight of a Baseball...

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Janus
Staff Emeritus