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

Answer:

Distance covered by B is 4 times distance covered by A

Explanation:

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

$s=\frac{1}{2}gt^2$

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

$s_A=\frac{1}{2}gt^2$

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

$s_B=\frac{1}{2}g(2t)^2 = 4(\frac{1}{2}gt^2)=4s_A$

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