is it 1 000 000 mm = 1km
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is it 1 000 000 mm = 1km
no couldn't be...Quote:
Originally posted by SeventhStar
is it 1 000 000 mm = 1km
may be the answer is: There are no grasshoppers 1m long.
come to think of it it could also be:
length and height are not connected so
answer is 1m
but if only size changes not strengh it wouldn't move an inch.
so answer could be: 0 m
Well, if you neglect air resistance and biology and stuff:Quote:
Originally posted by SeventhStar
well if the jump is proportional to the size I suppose 100 meters.
A 100*bigger grasshopper has a (100)³ bigger volume. Suppose its energy-production/volume has remained constant, the grasshopper could provide (100)³ times more energy in his jump and thus jump 1000.000 m high.
Sorry, forgot something. However, it's mass has also increased by (100)³ so a 1m grasshopper can also jump 1m high.
well what's the answer and whose turn is it
oh and who gets the point :) ;) :D
Wrong assumptions. Think harder. :DQuote:
Originally posted by Simon666
Well, if you neglect air resistance and biology and stuff:
A 100*bigger grasshopper has a (100)³ bigger volume. Suppose its energy-production/volume has remained constant, the grasshopper could provide (100)³ times more energy in his jump and thus jump 1000.000 m high.
Sorry, forgot something. However, it's mass has also increased by (100)³ so a 1m grasshopper can also jump 1m high.
oops ;)
so
Gabriel are you saying that neither my answers were right nor Simon's?
1.99 m?
Simon's answer is indeed correct, but his argumentation is wrong.Quote:
Originally posted by SeventhStar
oops ;)
so
Gabriel are you saying that neither my answers were right nor Simon's?
I don't see why. Let me reformulate it (litterally :D):Quote:
Originally posted by Gabriel Fleseriu
Simon's answer is indeed correct, but his argumentation is wrong.
Small grasshopper :
- E(produced for jump) = k * V1
- E(consumed by jump) = m1 * g * h1
Here are:
- k : energy production/volume, function of metabolism, presumed constant
- V1 : volume of small grass hopper
- m1 : mass of small grass hopper
- g : gravitational pull 9.81 m/s²
- h1 : height the small grass hopper can jump
Large grasshopper:
- E(produced for jump) = k * V2
- E(consumed by jump) = m2 * g * h2
Here are:
- k : still the same, doesn't change when upscaling
- V2 : volume of large grass hopper = (100)³ * V1
- m2 : mass of small grass hopper = (100)³ * m1
- h2 : height the large grass hopper can jump
Conservation of energy:
- k * V2 = m2 * g * h2
- k * (100)³ V1 = (100)³ m1 * g * h2
- h2 = k * V1 / (m1 * g) = h1
What's wrong with that?
My answer is that he would not jump at all as I have never seen a grasshopper that big !!!
I have never seen Xeon hopping in the grass either. And yes, I know a grass hopper is a bug. :D ;) :pQuote:
Originally posted by Elrond
My answer is that he would not jump at all as I have never seen a grasshopper that big !!!
I know that you know :rolleyes: but that is still a logical answer :) Let's wait to see if it's the correct one!Quote:
Originally posted by Simon666
I have never seen Xeon hopping in the grass either. And yes, I know a grass hopper is a bug. :D ;) :p
Ok, back to that grasshopper: muscular force is dependent on the section area, not on the muscular volume. Section area grows with the second power of the liniar dimension; mass with the third (as Simon correctly said). The question was not exactly a fair one, and the correct answer, if you want to take it strictly, is pretty complicated.
Assuming that the 1m grasshopper is built exactly like the small one (this assumption is implied in the question, or it wouldn't make sense), you have a 100 times smaller acceleration on a 100 times longer way that produces the lift-off speed.
I admit that it was not a very good question -- take a point from me or whatever. I thought I ask a question because it would have been the second time you had jumped my turn...
Ok, here we go. Simon, your turn, or whatever you guys decide. I go hide in the mountains...