How do you calculate the average jump height based on gravity and other forces?

[*Laurelindo*]

I was a bit curious as to how high you would be able to jump on other planets, but I don't really know how you calculate this;
for example, I am 6'2" tall (1,85 m) and weigh 200 lbs (91 kg), and usually jump about one foot (0,30 m) - how much force would I use for this?
And how would gravity and air friction affect my jump height?

[rubah]

force balance at the top of your jump: ∆F=0(not moving), F_jump+a_g*-h*m
F=9.81m/(s²)*91kg*(-.3m)
F=267.813 kg*m²/(s²)= 267.8N

267.8 newtons is the force you can exert, so
keeping F the same, and changing a_g to the gravity on whichever body you're interested in, (say 1.63, for the moon), solve for h
h=1.8m

basically just the earth's gravity divided by the gravity of where you'll be going. Air resistance is more complicated. You could imagine your body as an oval facing into the direction of the jump, then estimate a drag force, and add that to your F, but then you'd have to estimate how fast you're jumping and how relatively dense the atmospheres are on other planets, etc. Too much trouble, really

[*Laurelindo*]

force balance at the top of your jump: ∆F=0(not moving), F<SUB>jump</SUB>+a<SUB>g</SUB>*-h*m
F=9.81m/(s<SUP>2</SUP>)*91kg*(-.3m)
F=267.813 kg*m<SUP>2</SUP>/(s<SUP>2</SUP>)= 267.8N

267.8 newtons is the force you can exert, so
keeping F the same, and changing a<SUB>g</SUB> to the gravity on whichever body you're interested in, (say 1.63, for the moon), solve for h
h=1.8m

basically just the earth's gravity divided by the gravity of where you'll be going. Air resistance is more complicated. You could imagine your body as an oval facing into the direction of the jump, then estimate a drag force, and add that to your F, but then you'd have to estimate how fast you're jumping and how relatively dense the atmospheres are on other planets, etc. Too much trouble, reallyOk, thanks a lot.
So the formula would look like this then, right?

a<SUB>g</SUB>*-h*m + F<SUB>jump</SUB> = 0

By the way, how did you write "jump" and "g" like that? :eek:
I could just do it here because I copied your post.

[rubah]

&lt;sup>^super&lt;/sup>scripts and &lt;sub>_sub&lt;/sub>scripts

[Peegee]

&lt;sup>^super&lt;/sup>scripts and &lt;sub>_sub&lt;/sub>scripts



&lt;sup>^super&lt;/sup>scripts and &lt;sub>_sub&lt;/sub>scripts

as a general rule, you can see how a person made their post by quoting them.

SCIENCE THREAD

[*Laurelindo*]

^{^super}scripts and _{_sub}scripts



^{^super}scripts and _{_sub}scriptsas a general rule, you can see how a person made their post by quoting them.

SCIENCE THREADI tried that, but for some reason I get the exact post as the quote instead of the tags that were used.

Also, random test: Super^fun is_what it^is.

[Mirage]

Do you really need to know the air resistance though? Does it really make a significant difference in a jump? I would think I would struggle to jump even one centimeter higher in a vaccuum than I do normally.

[blackmage_nuke]

I would struggle to jump in a vaccuum at all seeing as i need to breathe.

[Mirage]

You pussy.

[Peegee]

Do you really need to know the air resistance though? Does it really make a significant difference in a jump? I would think I would struggle to jump even one centimeter higher in a vaccuum than I do normally.

Try jumping in a tornado

[Mirage]

Why? :(

[o_O]

You haven't truly jumped until you've jumped on a neutron star.

[Mirage]

I think i did that once.

[*Laurelindo*]

Do you really need to know the air resistance though? Does it really make a significant difference in a jump? I would think I would struggle to jump even one centimeter higher in a vaccuum than I do normally.I guess not, although it does make a certain difference depending on how high you jump. :jess:

I also heard that you could use this equation as well, if you leave out gravity:

H<SUB>x</SUB> = H<SUB>Earth </SUB>/ g<SUB>x</SUB>
<SUB></SUB>
<SUB></SUB>
H<SUB>x</SUB> = height you jump on planet x
H<SUB>Earth</SUB> = height you jump on Earth (obviously)
g<SUB>x</SUB> = the g-force on planet x

[rubah]

The g in g-force stands for gravity, you know

[Rostum]

Ah! Maths! *head explodes*

[*Laurelindo*]

The g in g-force stands for gravity, you knowI might have been a bit unclear in my last post, the 0,165 was simply the result of 1,62 ÷ 9,81;
g<SUB>1</SUB>h<SUB>1</SUB> = g<SUB>2</SUB>h<SUB>2</SUB> ↔ h<SUB>1</SUB> = h<SUB>2</SUB> http://upload.wikimedia.org/math/e/9/9/e99f03344ab9722020e7382af4e0a200.png (g<SUB>2 </SUB>÷ g<SUB>1</SUB>), where g<SUB>2 </SUB>÷ g<SUB>1</SUB><SUB> </SUB>in this case is 0,165.
Easier calculations.
<SUB></SUB>


Ah! Maths! *head explodes*Math and physics is fun, it's not so complicated and mysterious as you might think; remember that math and physics is always as clear and simple as possible, and most mathematicians and physicists encourage simplicity. :p

By the way...

Would you agree that math should be considered as "ingredients" for understanding physics?
I had a discussion about this with a friend who's very skilled in physics the other day, and we sort of agreed that math felt like something you read in order to be able to understand physics and that physics was a more complicated version of math.
Or should they be considered two completely separate things?

Th reason I'm wondering this is because physicists are always skilled in math, but mathematicians aren't necessarily skilled in physics.

[rubah]

when you say "leave out gravity" that implies not using the gravitational force or any multiple of it :p

I wouldn't say necessarily that physicists are "skilled" at math; they just use math as a tool to explain physics. They don't go poking at the borders of geometry and number theory or anything, they just use regressions, probability, differential equations etc to model things they observe in the universe. They do take higher math courses than say your average art historian, but they don't usually dig any deeper into the subjects. Engineers do the same thing with physics, using physics (and by association, math) to describe things that happen in their specific fields.

[*Laurelindo*]

when you say "leave out gravity" that implies not using the gravitational force or any multiple of it :p

I wouldn't say necessarily that physicists are "skilled" at math; they just use math as a tool to explain physics. They don't go poking at the borders of geometry and number theory or anything, they just use regressions, probability, differential equations etc to model things they observe in the universe. They do take higher math courses than say your average art historian, but they don't usually dig any deeper into the subjects. Engineers do the same thing with physics, using physics (and by association, math) to describe things that happen in their specific fields.I guess you're right.
Those mathematical formulas I remember them bringing up were mostly trigonometry (for calculating spectral colours etc) and derivatives.
I don't know what the high-school math courses are called in America, but in Sweden they are split up into "Course A", "Course B" etc, where Course A is obviously the easiest one.
They might have used a few formulas from Course D as well a few times (differential- and integral calculations).