Uncertainty Help: Homework Statement on Measuring a Projectile's Range

[flyflyfly37]

Homework Statement

Students decide to measure a projectile's range for an initial projectile angle of 45°. This angle has many advantages, not the least being that since the expression for the range is proportional to the sine of twice this angle, errors in determining the angle do not contribute to errors in the range.

As before, they make measurements to determine the initial speed. This time they find the initial speed to be 3.76 m/s with a relative uncertainty of 2.7%.

What is the uncertainty in the predicted range? [Remember that you can treat the uncertainty in the sin(2) factor as zero since it contributes no errors at 45°.]

_____ cm

Homework Equations

The Attempt at a Solution

I found the range to be 144cm and multiplied that by 2.7% to get 3.89 cm. But that's apparently not the right answer.

 

[jackarms]

I think your only problem is that 2.7% is the uncertainty of the velocity, which is going to be different from the uncertainty of the range. Solve for range in terms of the velocity, and then essentially you can replace the velocity with the uncertainty to find the range's error.

 

[flyflyfly37]

I also tried that.

2.7% of 3.76 is 0.10, so the two velocities are 3.66 and 3.86.
I found the respective ranges, 137cm and 152cm. subtracted the two to get 15cm then divided by 2 to find the uncertainty, which was 7.5. Plugged it in, still not right. Am i doing things wrong?

 

[jackarms]

Are you sure it's absolute uncertainty rather than relative uncertainty like you have for the velocity? Otherwise, I'd guess it's a rounding error. Could you also write down an expression for the range as a function of the initial velocity, without anything plugged in? I'll show you a better way to solve it.

 

[haruspex]

I also tried that.

2.7% of 3.76 is 0.10, so the two velocities are 3.66 and 3.86.
I found the respective ranges, 137cm and 152cm. subtracted the two to get 15cm then divided by 2 to find the uncertainty, which was 7.5. Plugged it in, still not right. Am i doing things wrong?

You tried assuming the relative uncertainty in range was also 2.7%. You tried the absolute error version of the same. Then you tried the absolute error worked out from your equation, so making no assumptions, and you got a different result. This shows your 2.7% assumption was wrong.
That leaves one combination you haven't tried.

 

[flyflyfly37]

You tried assuming the relative uncertainty in range was also 2.7%. You tried the absolute error version of the same. Then you tried the absolute error worked out from your equation, so making no assumptions, and you got a different result. This shows your 2.7% assumption was wrong.
That leaves one combination you haven't tried.

Thanks, but I'm little bit confused what you meant.

 

[haruspex]

Thanks, but I'm little bit confused what you meant.

Using the equation, what do you get for the relative error?