Question

Two objects are dropped from rest from the same height. Object A falls through a distance during a time t, and object B falls through a distance during a time 2t. If air resistance is negligible, what is the relationship between A and B?

Answer 1

Distance covered by B is 4 times distance covered by A

Step-by-step explanation:

For an object in free fall starting from rest, the distance covered by the object in a time t is

`s=(1)/(2)gt^2`

where

s is the distance covered

g is the acceleration due to gravity

t is the time elapsed

In this problem:

- Object A falls through a distance
`s_A` during a time t, so the distance covered by object A is

`s_A=(1)/(2)gt^2`

- Object B falls through a distance
`s_B` during a time 2t, so the distance covered by object B is

`s_B=(1)/(2)g(2t)^2 = 4((1)/(2)gt^2)=4s_A`

So, the distance covered by object B is 4 times the distance covered by object A.