Final answer:
Using the second equation of motion, an object dropped from a height of 10 m on the Moon takes 3.49 seconds to hit the lunar surface, we calculated the acceleration to be approximately 1.64 m/s², and thus, the best approximate answer is B. 1.00 m/s².
Step-by-step explanation:
To calculate the acceleration due to gravity on the Moon, we can use the second equation of motion which relates distance (s), acceleration (a), and time (t): s = (1/2)×a×t². Here, the distance s is 10 m (the height from which the object is dropped), and the time t is 3.49 s. We can rearrange the equation to solve for a: a = (2×s) / t².
Substituting the given values, we get a = (2× 10 m) / (3.49 s)² = 20 m / 12.1801 s² = 1.64 m/s². However, since none of the options exactly match this calculated value, we will have to select the closest one. The closest option is A. 2.84 m/s², but based on our calculation and the known fact that the acceleration due to gravity on the moon is approximately 1.6 m/s², we are likely looking for the nearest approximation among the choices given.
Therefore, the most appropriate answer to select, given the options provided, is B. 1.00 m/s²