Question

My Notes 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?

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.

Answer 1

Answer:

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

Explanation:

M = Mass of Earth = 5.972×10²⁴ kg

r = 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

$ma=G\frac{Mm}{r^2}\\\Rightarrow a=G\frac{M}{r^2}\\\Rightarrow a=6.67\times 10^{-11}\frac{5.972\times 10^{24}}{(6.371\times 10^6)^2}\\\Rightarrow a=9.81364\ m/s^2$

From the equation above it can be seen that all objects irrespective of mass falls at the same acceleration.

$s=ut+\frac{1}{2}at^2\\\Rightarrow 1=0t+\frac{1}{2}\times 9.81364\times t^2\\\Rightarrow t=\sqrt{\frac{2s}{9.81364}}$

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