# Slingshot Projectile Physics



## Darb (Sep 14, 2010)

Ok, call me insane, but sometimes when I have insomnia, I find that doing something that forces my brain to focus helps me to purge the random thoughts of the day, and relax enough to go back to bed. In this instance, I decided to play a little with ballistic physics.



> *Projectile Motion Physics Problem: I shoot a 3/8" steel ball bearing (3.55 grams) 190 fps (58 m/s) at 40 degree inclination.*
> 
> a) How long does it take to reach maximum height ?
> 
> ...


Assumptions: To keep this simple, we're doing this at Earth normal (sea level) gravity, level ground, in a vaccum (sorry - I haven't learned how to figure in air resistance). Note also that since we're assuming no air resistance, the size and mass of the ball become irrelevant &#8230; only the velocity and angle matter here. 

The first step is to take the velocity and angle, and decompose it into its vertical and horizontal components, and define thouse as the Initial conditions:

v[sub]iv[/sub] (Initial Velocity, Vertical Component) = 58 x Sin(40) = 37.28 m/s

v[sub]ih[/sub] (Initial Velocity, Horizontal Component) = 58 x Cos(40) = 44.43 m/s

And of course, there's a negative acceleration of 9.8 m/s/s eating away at the vertical velocity.

*a) How long does it take to reach maximum height ?*

Answer: To derive the time it takes to reach maximum height (top of trajectory arc), we set the final vertical velocity to zero and solve:

a = (v[sub]fv[/sub] - v[sub]iv[/sub])/t, therefore

t = (v[sub]fv[/sub] - v[sub]iv[/sub])/a = (0 - 37.28)/-9.8 = *3.8 seconds*

BTW, total transit time is simply double the time it takes to reach maximum elevation, or 7.6 seconds.

*b} What is the maximum height of its trajectory ?*

Answer: For deriving max height:

d = v[sub]iv[/sub]t + (0.5)at[sup]2[/sup] = 37.28 x 3.8 + (0.5) x 9.8 x (3.8)[sup]2[/sup] = *70.908 meters*

*c) How far away will it land ?*

Answer: We do the same as for the above, except for the horizontal component.

d = v[sub]ih[/sub]t + (0.5)at[sup]2[/sup] = 44.43 x 3.8 + (0.5) x 9.8 x (3.8)[sup]2[/sup] = *98.078 meters*

And on that note, I'm going back to bed.


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## NoSugarRob (Jun 3, 2010)

.


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## A+ Slingshots (Jan 22, 2010)

.... wrong thread..... I'm backin' out of here quickly before my brain in irreparably injured!!!!


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## Darb (Sep 14, 2010)

Say, I wonder if this blind unreasoning aversion to math will work against thieves and rapists ?

_Rapist: Ok lady, gimme some sugah an I won't haftah hurtya !








Female Jogger: Did you know that the Tangent of 90 degrees is Infinity ?
Rapist: Eh ?








Female Jogger: Speaking of infinity, did you know that there's meaningful difference between "Transfinite Numbers" and "Absolute Infinity" ?
Rapist: {clutching head in pain} Make it stop ...






















Female Jogger: Not only that, but some philosopher-Mathematicians back in ancient Greece postulated that there are different numerical subdivisions or types of Infinity. Aristotle, for instance differentiated between "Potential" and "Actual" Infinity, and some mathematical texts in ancient India differentiated between "Nearly" Infinite, "Truly" Infinite, and "Infinitely" Infinite. This is not to be confused with the transfinite numbers I mentioned earlier ... such as Aelph Naught, Aelph One, Aelph-W, and Aelph-Alpha, which pertain to Set Theory, and deal with infinite sets using transfinite numbers.
Rapist: Help ! Police ! {runs}
Female Jogger:







{resumes jogging}_


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## A+ Slingshots (Jan 22, 2010)

Darb said:


> Say, I wonder if this blind unreasoning aversion to math will work against thieves and rapists ?
> 
> _Rapist: Ok lady, gimme some sugah an I won't haftah hurtya !
> 
> ...


*LOL!!! Great joke Darb!!! However, my aversion to math is neither blind nor unreasoned.... With my eyes fully open, as well as the understanding (such that it is) of my mind, I have reasoned without a doubt, based on ample evidence that I am terrible at mathematics.... though strangely enough, the history of mathematics and mathematicians fascinates me.... go figure the human mind!!!







* *None-the-less, I have stayed way too long again.... those equasions above are making me feel a bit queezy!!!! *
*Once again I take my leave.....







RUN AWAY!!!!!!.... RUN AWAY!!!......... accompanied by the faux sound of horses hooves made by coconuts!!!!!







*


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