A student measures the time taken for a stone to fall from a cliff. The recorded readings are 9.8 s , 9.9 s , 10.1 s , and 10.2 s . The student uses the formula h = 1 2 gt^2 to calculate the height of the cliff. Assuming the acceleration due to gravity g is known exactly, what is the percentage error in the calculated height?

Step-by-step solution

First, find the mean value of the time measurements: t_ mean = 9.8 + 9.9 + 10.1 + 10.2 4 = 40.0 4 = 10.0 s . Next, calculate the absolute errors for each reading: t₁ = |9.8 - 10.0| = 0.2 s t₂ = |9.9 - 10.0| = 0.1 s t₃ = |10.1 - 10.0| = 0.1 s t₄ = |10.2 - 10.0| = 0.2 s The mean absolute error in time is: t_ mean = 0.2 + 0.1 + 0.1 + 0.2 4 = 0.6 4 = 0.15 s . The percentage error in the time measurement is: t_ mean t_ mean 100 = 0.15 10.0 100 = 1.5 % . The height is calculated using h = 1 2 gt^2 . Since g and 1 2 are e