Can I Throw a Ball 120 Feet in My Office Without Hitting the Ceiling?

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Discussion Overview

The discussion revolves around the feasibility of throwing a baseball 120 feet in an office setting without hitting the ceiling, considering factors such as launch height, speed, and trajectory. Participants explore the physics involved in the throw, including calculations related to time of flight and the effects of backspin on the ball's trajectory.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant suggests calculating the time it takes for a ball to fall from the ceiling to determine the necessary horizontal velocity for the throw.
  • Another participant provides a formula for calculating the time of fall based on the height of the ceiling and gravity, estimating a required speed of over 60 ft/s or 40 mph.
  • A different viewpoint emphasizes the complexity of the throw, noting that the release height affects the required speed, with specific calculations provided for different release heights.
  • Some participants discuss the potential benefits of using a denser ball to minimize air resistance and improve accuracy in calculations.
  • There is a suggestion to consider bouncing the ball off the floor as part of the throw, which could alter the dynamics of the throw.
  • One participant explains how backspin can affect the trajectory of a baseball, allowing it to travel further with less drop.
  • Another participant raises the challenge of ensuring the ball hits the wall at a specific height, prompting further calculations for the required speed.
  • Concerns about personal throwing limits and accuracy are expressed, with some participants indicating they may not be able to achieve the necessary speeds.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the feasibility of the throw, as various factors such as launch height, speed, and technique are debated. Multiple competing views and calculations are presented, indicating uncertainty in the exact requirements for successfully throwing the ball without hitting the ceiling.

Contextual Notes

Limitations include assumptions about the release height of the ball, the effects of air resistance, and the accuracy of the calculations based on varying throwing techniques. The discussion does not resolve these complexities.

Who May Find This Useful

Individuals interested in physics, particularly in the context of projectile motion, as well as those curious about practical applications of physics in everyday scenarios.

DrakeMK3
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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.
 
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.
 
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.
 
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 traveling 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.
 
  • #10
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/

Especially the part about The Effect of Spin on the Flight of a Baseball...
 
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  • #11
DrakeMK3 said:
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.

Then the "fall" time will equal the "rise" time from 4 feet, and the needed speed is is 58 mph.
 
  • #12
Since I can only throw about 70 mph, this is quickly approaching my personal limits combined with accuracy. Some of the other guys can throw harder than I can, so I'm sure they'd be better at this test. At the back of our office we have a large brick wall that we are probably going to use as a test subject and visually judge the 12ft. ceiling.
 

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