Conundrum – physics help please

[The Statman]

"If two synchronised trampolinists leave the bed of the trampoline at exactly the same time, and return to the bed at the same time, is it possible for them to have attained different heights, all other things being equal?"

Help!

So, assuming that they are completely identical twins and the trampolines are strung identically, is it possible for one to cover more distance (upwards and back again) from exactly the same start time to exactly the same finish?

[MrRottweiler]

In a controlled experiment like that where all the variables are the same I would say not. Wait for Albert to sign on and see what he says!

[hegeland]

If "they are completely identical twins and the trampolines are strung identically", we can assume that their initial velocity are identical. We ignore air resistance.

If they spend the same amount of time in the air and have the same initial velocity they cannot reach different distances Y-ways.

If we makethe distance Y-ways a function of time, like

s(t) = (V0 * sin (angle)) + ((g*t2)/2)

and set two different angles, like 20 degrees and 60 degrees, the curves looks something like this:

E. Charlton.jpg

[slayericed]

If they spend the same amount of time in the air and have the same initial velocity they cannot reach different distances Y-ways.

Actually the amount of time in air depends on the initial velocity and the force acting on the system which is gravity in this case and hence is constant, so in reality the only independent variable is the initial velocity, the time to fallback and the highest point reached all depend on the initial velocity.

Statman I am sure u must be aware of the basic equations of motion. You can use them to prove that it is NOT possible to travel different distances in the same time duration under a system which experiences a constant force (like gravity in this case).

Another way u can convince urself is by exaggerating the experiment

say the two trampolinists travel wildly contrasting distances , one does around 1 M another one does 100 M i know this doesnt make sense but bear with me for a moment, ok now u are imagining the scenario in ur head, to get to a height of 100 m the trampolinist must have a pretty high initial velocity AND to get back to ground level in the same time as the other one, there must be some force pulling him down quite hard or else there is no way he can make it back in the same time, which my friend is not possible because they experience the same downward force, gravity.

So now after scaling up and seeing that it is not possible for that particular scenario, u must realize that for any case if they reach back at the same time, they must have travelled the same vertical distance.

please tell me if u need the mathematical treatment for this.

HTH

[elvaago]

The only way I can see this happening if one of them pulls up his legs during the jump and releases his legs again on the way down. I mean, gravity works the same for everyone.