Question

If a baseball, a basketball, and a 71.2 N shot were dropped simultaneously from the top of the Empire State Building (and air resistance was not a factor), which would hit the ground first?

Answer 1

The objects will reach the ground at the same time

Step-by-step explanation:

m = Mass of object

a = Acceleration

m = Mass of the Earth = 5.972 × 10²⁴ kg

G = Gravitational constant = 6.67 × 10⁻¹¹ m³/kgs²

R = Radius of Earth = 6371000 m

The weight of an object balances the gravitational force

`ma=(GMm)/(R^2)`

The mass of the of any object gets cancelled

`\\\Rightarrow a=(GM)/(R^2)\\\Rightarrow a=(6.67* 10^(-11)* 5.972* 10^(24))/((6.371* 10^(6))^2)\\\Rightarrow a=9.81364\ m/s^2`

All objects irrespective of their weight will fall with the acceleration equal to 9.81364 m/s².

So, here the baseball, basketball, and the 71.2 N shot will hit the ground at almost the same time. There will be little variation due to the surface area of each body but will mostly reach the ground at the same time.