Question

Two identical objects A and B fall from rest from different heights to the ground. If object B takes twice as long as object A to reach the ground, what is the ratio of the heights from which A and B fell

Answer 1

Answer:

1:4

Explanation:

We have, two identical objects A and B fall from rest from different heights to the ground.

Object B takes twice as long as object A to reach the ground. It is required to find the ratio of the heights from which A and B fell. Let $h_A\ \text{and}\ h_B$ are the height for A and B respectively. So,

$\dfrac{h_A}{h_B}=\dfrac{(1/2)gt_A^2}{(1/2)gt_B^2}\\\\\dfrac{h_A}{h_B}=\dfrac{t_A^2}{t_B^2}$

We have,

$t_B=2t_A$

So,

$\dfrac{h_A}{h_B}=\dfrac{t_A^2}{(2t_B)^2}\\\\\dfrac{h_A}{h_B}=\dfrac{1}{4}$

So, the ratio of the heights from which A and B fell is 1:4.