Final answer:
The percentage uncertainty in the displacement s of a freely falling ball can be found by combining the uncertainties in time t and acceleration g. The calculation involves doubling the percentage uncertainty of the squared time (6%) and adding it to the uncertainty in g (2%), resulting in a total uncertainty of ±8%.
Step-by-step explanation:
To calculate the percentage uncertainty in the displacement s when a ball falls freely with acceleration g and the variation with time t of its displacement is given by the equation s = 1/2gt^2, we need to use the given percentage uncertainties in t and g. We know that the percentage uncertainties in t and g are ±3% and ±2% respectively.
Since the equation for displacement is a product of t squared and g, we can use the rule for combining uncertainties for multiplication and powers. The percentage uncertainty for a variable raised to a power is the percentage uncertainty in that variable times the power. For the time t squared that would be 2 * 3% = 6%. Since the uncertainty in g is 2%, the total percentage uncertainty in s is the sum of the uncertainties in g and t squared, which is 6% + 2% = ±8%. Therefore, the correct answer is C. ±8%.