Final answer:
The speed with which a stone strikes the ground when dropped from the top of the Empire State Building, with negligible air resistance, is found using the equation of motion v= √(2gh), which yields approximately 93.15 m/s. Thus, the correct answer is the closest option which is (a) 94.1 m/s.
Step-by-step explanation:
To determine the speed with which the stone strikes the ground when dropped from the top of the Empire State Building (height 443 m), we can use the equations of motion for an object in free fall assuming negligible air resistance and acceleration due to gravity (g) of 9.8 m/s2.
The equation v2 = u2 + 2gs can be applied, where v is the final velocity, u is the initial velocity (0 m/s since it's dropped from rest), g is the acceleration due to gravity, and s is the distance fallen.
Substituting the known values, we get:
v2 = 0 + 2 * 9.8 m/s2 * 443 m
v2 = 8676.4 m2/s2
v = √8676.4 m2/s2
v ≈ 93.15 m/s
Thus, the correct answer is (a) 94.1 m/s, which is closest to our calculated value. This shows that the final speed of an object in free fall is independent of its mass and primarily determined by its initial height and acceleration due to gravity.