For an experiment in this unit, you measure the time of a ball falling from rest as 3.4 ± 0.2 s and you want to calculate the distance the ball has fallen during that time, where you are taking the acceleration due to gravity as a = 9.8 ± 0.1 ms-2. What is the absolute uncertainty (to 1 sig fig) in the distance, calculated from the given values? Question 10) Select one: a. 4 m b. 0.5 m c. 7 m d. 6 m e. 0.3 m
Question
For an experiment in this unit, you measure the time of a ball falling from rest as 3.4 ± 0.2 s and you want to calculate the distance the ball has fallen during that time, where you are taking the acceleration due to gravity as a = 9.8 ± 0.1 ms-2. What is the absolute uncertainty (to 1 sig fig) in the distance, calculated from the given values?
Question 10) Select one:
a. 4 m
b. 0.5 m
c. 7 m
d. 6 m
e. 0.3 m
Solution
To calculate the absolute uncertainty in the distance, we first need to calculate the distance itself using the equation of motion: d = 0.5at^2.
Given: a = 9.8 ± 0.1 ms^-2 t = 3.4 ± 0.2 s
Substituting these values into the equation, we get:
d = 0.5 * 9.8 * (3.4)^2 = 56.532 m
Next, we calculate the absolute uncertainty in the distance using the formula for the propagation of uncertainty:
Δd = sqrt[(0.5t^2Δa)^2 + (atΔt)^2]
Substituting the given values into this equation, we get:
Δd = sqrt[(0.53.4^20.1)^2 + (9.83.40.2)^2] = 6.7 m
So, the absolute uncertainty in the distance, to 1 significant figure, is approximately 7 m. Therefore, the correct answer is:
c. 7 m
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