You can calculate the time it will take for an object to fall from the top of a building to the ground if you know the height of the building. If the height has an uncertainty of 1.0% ,what is the uncertainty in time?

Short Answer

Expert verified

The uncertainty in time is 0.5 %

Step by step solution

01

About Uncertainty for powers and roots

For the function y=xa the relative uncertainty in y(%ey)is t times the relative uncertainty in x(%ex)

y=xa

%ey=a%ex

02

Calculate the amount of time it takes for an object to fall from a building to the ground

Given information:

An object falls from the top of a building to a known height on the ground.

The uncertainty in height is 1.0 %

Calculation of time uncertainty:

Consider an object falling from a height of1/2gt2in time t.

Now, use the required formula:

y=xa%ey=a%ex

Height =1/2gt2

Here, $a=$2

%ey=a%ex%eheight=2(%etime)1.0%=2%etime

Now, rearrange the above formed value as shown,

%etime=1.0%2=0.5%

Therefore, the uncertainty in time is 0.5%

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