Question

Uncertainty Question

Answer 1

Say I have three velocities

\[V_x,V_y,V_z\]

in such a function

\[f(V_x,V_y,V_z)\]

and i want to find the uncertainty

I'm given the

\[U_t,U_d\] do i simply count the velocities x,y,and z as a toal velocity uncerrtainty

Answer 2

or do i have to have

\[U_{t_x},U_{t_y},U_{t_z}\]

Answer 3

Is f a function of t and d as well as\[ v _{x}, v _{y} , v _{z}\]?

Answer 4

well yes because it's average velocity

Answer 5

What is the explicit for of the function.

Answer 6

no as in 3 different avg velocities

Answer 7

I need to know how to find the uncertainty of a function that has 3 different velocities within it. Do i take the derivative for each term so the derivative of x , derivative of y and the derivative of z , do i split it up into distance and time or do i find the uncertainty uncertainties of the 3 velocities and then use those for the final equation

Answer 8

Ok
\[df =\sum_{i=1}^{3} \left( \frac{ df }{ dv _{i} } \right)dv _{i}\] and the uncertaintly in f is\[\Delta f=\sqrt{\sum_{i=1}^{3}\left( \frac{ df }{dv _{i} } \right)^{2}\left( dv _{i} \right)^{2}}\]

Answer 9

not quite what i'm looking for say i had a function

\[f(x)=\frac{v_1+v_2(v_3^3)}{YG^2}\]

how do i find hte uncertainty of this... Since the uncertainty in time and distance are the same for each one of hte velocities, should i find the Uncertainties of all the velocities and then find the partials (leave as is ) or should i change everything to d/t since those are the terms i have uncertainties for

Answer 10

You usually express the uncertainty of the function in terms of the uncertainty of the measurable quantities on which it depends.If you know dvi then that is what you use.

Answer 11

Uncertainty Ut is to what decimal place of time that i go too.

Answer 12

yes @gleem but when i take the derivatives of all when i make them make d/t .... it becomes some weird units that i believe is completely wrong

Answer 13

For example meters per second, or kilometers per second so the Uncertainty is going to be 1 second or 1 kilometer

Answer 14

Uncertainty for Ud is the same as Ut.

Answer 15

http://www.youtube.com/watch?v=uVixRxsokSc

Answer 16

ahh true i guess the units are pretty messed up hten..... i'm getting like d^3/2 and stuff lol

Answer 17

your function is not dimensionally correct. In the numerator for example you mix m/s and m^3/sec^3. that has to be fixed.

Answer 18

\[\pm m/s\]

Answer 19

the uncertainties are how accurate our measuring devices and how accurate our formulas are

Answer 20

for example g=10 \[\pm 0.2\]

Answer 21

http://www.youtube.com/watch?v=_UAp5n5lVRE

Answer 22

Both formulas are correct Outkast3r09 and gleem but after adding all the numbers using your formulas i am still missing +- of the percent of air so final answer for me is f, t, d = + or- 1%/etc

Answer 23

Please tell me the meaning of f(v). is it the range of a cannon with air resistance taken into account?

Answer 24

the cannon was the tool not the formulas

Answer 25

if i shot my cannon i need the t,d,f to see if i hit the target
the uncertainty of \[t =d,f\]

Answer 26

If the formula is for the range of a cannon all you need is the elevation of the barrel and the muzzle velocity. They are the independent variables. Time and distance are determined.

Answer 27

what are mistakes in drawing