Q. A ball falls freely from rest with an acceleration g. The variation with time t of its displacement s is given by s = 1/2 gt^2. The percentage uncertainty in the value of t is ±3% and that in the value of g is ±2%. Calculate the percentage uncertainty in the value of s.
A. Δs/s = Δg/g + 2 Δt/t = 0.02 + (2 × 0.03) = 0.08 = ±8%
Question of the day
Can you explain why in the answer the fractional uncertainty for time (Δt/t) is multiplied by 2 before being added to the fractional uncertainty for gravity (Δg/g)?