Final answer:
The local acceleration of gravity is approximately 22.87 ft/s². Therefore, the local acceleration of gravity is approximately 22.87 ft/s^2.
Step-by-step explanation:
In order to determine the local acceleration of gravity, we can use the formula w = mg, where w represents weight, m represents mass, and g represents the acceleration due to gravity.
Given that the person's mass is 214 lbm and their weight is 152 lbf, we can convert the units to the metric system for easier calculations. 1 lbm is approximately 0.4536 kg and 1 lbf is approximately 4.448 N.
Therefore, the mass is approximately 96.94 kg (214 lbm x 0.4536 kg/lbm) and the weight is approximately 675.89 N (152 lbf x 4.448 N/lbf).
Now we can use the formula w = mg to find the acceleration due to gravity.
Rearranging the formula, we get g = w/m. Substituting the values, we have g = 675.89 N / 96.94 kg.
Calculating this gives us an approximate value of g = 6.97 m/s^2.
To convert this to ft/s^2, we can use the conversion factor 1 m/s^2 = 3.28 ft/s^2.
Therefore, the local acceleration of gravity is approximately 22.87 ft/s^2.