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

1:4

Step-by-step 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,

`(h_A)/(h_B)=((1/2)gt_A^2)/((1/2)gt_B^2)\\\\(h_A)/(h_B)=(t_A^2)/(t_B^2)`

We have,

`t_B=2t_A`

So,

`(h_A)/(h_B)=(t_A^2)/((2t_B)^2)\\\\(h_A)/(h_B)=(1)/(4)`

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