Two identical objects A and B fall from rest from different heights to the ground and feel no appreciable air resistance. 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? A) h_A/h_B = 1/ B) h_A/h_B = 1/2 C) h_A/h_B = 1/4 D) h_A/h_B = 1/8

Question

Quizplus · Accepted Answer

Let h be the height from which objects A and B were dropped.
According to kinematic equation of motion for free fall, 
h = 1/2 gt^2, where t is the time of fall and g is the acceleration due to gravity.
Since objects A and B have the same acceleration, we can write
hA = 1/2 g tA^2 and hB = 1/2 g tB^2
Given, tB = 2tA
hB/hA = (1/2 g tB^2) / (1/2 g tA^2) = (tB/tA)^2 = 4
Therefore, hB = hA/4, which means the ratio of the heights from which A and B were dropped is 1:4.
So, the answer is C.

Two Identical Objects a and B Fall from Rest from Different