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 the height from which A is dropped be hA and from B be hB.
From the equations of motion, we know that the time taken for an object to fall from rest is given by:
t = √(2h/g), where h is the height and g is acceleration due to gravity.
For object A, time taken = tA = √(2hA/g)
For object B, time taken = tB = √(2hB/g)
Given that tB = 2tA.
Substituting time equation of A and B:
√(2hB/g) = 2√(2hA/g)
Squaring both sides:
(2hB/g) = 4(2hA/g)
hB/hA = 1/4
Therefore, hA/hB = 4
Hence, the correct choice is (C) hA/hB = 1/4.

Two Identical Objects a and B Fall from Rest from Different