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, really

Ok, 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?
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><sup>super</sup>&lt;/sup>scripts and &lt;sub><sub>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

	

		

			

			
				
				
<sup><sup>super</sup></sup>scripts and <sub><sub>sub</sub></sub>scripts
			
		
	

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

SCIENCE THREAD

I 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.

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