Question

analyzing gravitational data quick check
melissa is working on the roof of her house. she drops a hammer and a nail. why do both objects hit the ground at the same time? (1 point)
air resistance causes both objects to fall at the same rate.
earths gravity causes both objects to fall at the same rate.
drag causes both objects to fall at the same rate.
velocity causes both objects to fall at the same rate.

Explanation:

When objects are in free - fall near the Earth's surface (assuming air resistance is negligible or in a vacuum - like situation as is often the case in basic physics problems about falling objects), the acceleration due to Earth's gravity (\(g\approx9.8\ m/s^{2}\)) acts on them. The acceleration of an object in free - fall is given by the formula \(a = g=\frac{F}{m}\), where \(F = mg\) (the force of gravity). The mass \(m\) cancels out (\(a=\frac{mg}{m}=g\)), meaning that the acceleration of an object in free - fall near the Earth's surface is independent of its mass. Air resistance (or drag) would actually cause objects with different surface areas and masses to fall at different rates if it were significant. Velocity is a result of the acceleration due to gravity acting over time, not the cause of objects falling at the same rate.

Answer:

Earth’s gravity causes both objects to fall at the same rate.