# Physics question

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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 3.22 m/s with a relative uncertainty of 2.4%.

(a)What is the predicted range?
(b)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°.]

They launch the ball ten times and find the results for the range in centimeters to be 109.5, 109.6, 106.8, 112.5, 111.3, 106.5, 116.5, 110.1, 109.0, and 111.5.

(a)iv) What is the uncertainty in any single range measurement? [Hint: Think "standard deviation of measured values".]
(b)What is the standard error of the mean in the average range?
(c)Suppose the launch angle were the same for all ten trials, but only known (measured) to 1.3% . You would then expect the angular uncertainty to increase the spread in the measured range values by:

• Physics question -

The average range is calculated to be 105.8

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