Answer:
8.2 m/s
Explanation:
The horizontal component of the velocity is given by:
where
v = 10 m/s is the magnitude of the velocity
is the angle at which the ball has been thrown, with respect to the horizontal
Substituting the values into the equation, we get
Maximum error in the result of the sum of measurement is equal to the sum absolute error of the individual observed measurements
(a) The maximum error in D is 0.09
(b) The standard error in D is approximately 0.034
The procedure for arriving at the above values is as follows;
The given measurements and the sited errors are;
A = 15.21 + 0.01
B = 10.82 + 0.05
C = 11.00 + 0.03
D = A + B + C
(a) Required parameter;
To calculate the maximum error in D
The equation for the propagation of error in addition is presented as follows;
Given that we have;
x = a + b
Therefore;
x + ±Δx = (a ± Δa) + (b ± Δb) = a + b ± (Δa + Δb)
∴ Δx = Δa + Δb
From the above formula, we have;
Where;
D = A + B + C
The maximum error in D = The sum of the maximum error in A, B, C
∴ The maximum error in D = 0.01 + 0.05 + 0.03 = 0.09
(b) Required parameter:
To find the standard error in D
The standard error is the sampling distribution's standard deviation, SD
Variance = SD²
The combined variance, SD² = The sum of the squares of individual standard deviations
Given that the standard errors represents the standard deviation, we get;
The combined variance, SD² = 0.01² + 0.05² + 0.03²
The combined variance, SD = √(0.01² + 0.05² + 0.03²) = 0.059
Where n = 3, for the three measurement, we get;
The standard error in D is approximately 0.034
Learn more about maximum error and standard error here: