Maybe a dumb question on standard error in equations

AI Thread Summary
To evaluate the standard error in the velocity calculation using the formula v = sqrt(2*g*change in y), first calculate the velocity using the nominal value of change in y (12.10 cm). Then, determine the velocity using the upper (12.16 cm) and lower (12.04 cm) bounds by plugging these values into the formula. The average of these two velocities will provide a central value, while the difference between them can be used to estimate the standard error. An algebraic approximation can also be applied for small changes, using the formula sqrt(x + dx) to refine the error calculation. This method effectively incorporates the standard error into the final velocity result.
JazzyJones
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Homework Statement



I am using a value of change in y say 12.10 cm + or - .06cm.

I am trying to find velocity using the formula
v= sqrt(2*g*change in y)

how do I evaluate this equation with my standard error? because I can't just add or subtract the .06cm after since I will have a value for velocity now.

Homework Equations





The Attempt at a Solution

 
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Can you just plug in 12.10 cm to get v and then plug in 12.10 cm + .06cm and 12.10 cm - .06cm to figure out the error in v?
 
i'm not sure if this was correct but, I plugged in the value with + then plugged in te value with -. Average the two values, and did + or - the difference between the two
 
JazzyJones said:
i'm not sure if this was correct but, I plugged in the value with + then plugged in te value with -. Average the two values, and did + or - the difference between the two
That'll work. The algebraic way is to approximate sqrt(x + dx) = sqrt(x)sqrt(1+dx/x) as sqrt(x)(1+dx/2x) for small dx.
 

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