My Notes on Objects Falling from a Tall Building

The Scenario

A student throws a heavy red ball horizontally from a balcony of a tall building with an initial speed v0. At the same time, a second student drops a lighter blue ball from the same balcony. Neglecting air resistance, which statement is true?

The Options

A. The blue ball reaches the ground first.

B. The balls reach the ground at the same instant.

C. The red ball reaches the ground first.

D. Both balls hit the ground with the same speed. None of the above statements are true.

The Answer

Answer: B. The balls reach the ground at the same instant.

Explanation

M = Mass of Earth = 5.972×10²⁴ kgr

Radius of Earth = 6.371×10⁶ m

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

t = Time taken

u = Initial velocity v = Final velocity

s = Displacement

a = Acceleration

Calculations:

ma = G * (M * m) / r²

a = G * (M / r²)

a = 6.67 x 10^-11 * ((5.972 x 10^24) / (6.371 x 10^6)²)

a = 9.81364 m/s²

From the equation above, it can be seen that all objects fall at the same acceleration.

s = ut + (1/2)at²

1 = 0t + (1/2) * 9.81364 * t²

t = √(2s / 9.81364)

If both bodies are initially at rest and travel the same distance, the time taken for the bodies to reach the ground will be the same.

Is the acceleration due to gravity the same for objects of different masses?

Yes, the acceleration due to gravity is the same for all objects regardless of their masses. All objects fall at the same rate of acceleration towards the Earth.