An ball is dropped from 20.5m. It bounces once, falls back down,

>>8542421
Depends on the assumptions you make.

>>8542421
>an ball

>>8542663
Not on earth it doesn't.

>>8542421
gh=10*20.5=205 m^2/s^2
gh'=10*7.6=76 m^/s^2
205-76=129 m^2/s^2
/10m/s^2 = 12.9m

>>8542898
>205-76=129 m^2/s^2
>/10m/s^2 = 12.9m
What the fuck are you doing?

assume the energy lost is proportional to total energy by a factor of x
then 20*x^2=7
20*x =h , h being what we want to compute
7*20 =h^2
√(140) =h
h≈12m

>>8542920
also dude golden ratio lmao

>>8542913
Physics.

>>8542898
For some strange reason you have assumed that the ball has energy after the first impact equal to the difference between its initial energy and energy after the second impact. No basis for this and it makes no sense.

>>8542920
Thats a big assumption, but maybe needs to be assumed.

>>8542927
>Physics.
No you're not, you're banging numbers together and hoping you get an answer.

>>8542952
>Thats a big assumption, but maybe needs to be assumed.
It seems like a pretty reasonable assumption to me.

>>8542970
Seems like a pretty convenient assumption to me. With no knowledge of the ball you have no idea if its true, and without it you wouldnt be able to solve the problem with this method.

>>8542970
If you have some better way of showing it, please do. Your answer will be between 12 and 13. Otherwise you have no idea what you're doing, which is what i suspect.

States:
1: upon releasing the ball
2: instantaneously before impact
3: next max ascent
4: instantaneously before impact
5: next max ascent
[eqn] E_1 = mgh_1 = E_2 = 1/2 mv_2^2 [/eqn]
[eqn] E_3 = E_1 - X_{2-3} = mgh_3 = E_4 = 1/2 mv_4^2 [/eqn]
[eqn] E_5 = E_4 - X_{4-5} = mgh_4 [/eqn]
idk

Assuming exponential decay after each collision, I got 12.48m.

You have no model of the collision, so there's no way to really know.

I put the upper bound at 20.5 meters.

>>8545242
What's 'exponential decay'?

>>8545265
I suppose that the general energy drop follows an exponensial form.

>>8545265
https://en.m.wikipedia.org/wiki/Exponential_decay

12.5m

>>8542920
best solution so far
apply principle, use 'ruthless rounding', get sanity check for detailed calculation.

popular exam question: will it bounce forever? if not, how long?
answer: the number of bounces is not limited but the time is.
(in OP's case it would bounce for about 16 seconds)