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? Neglect air resistance. A) h_A/h_B = 1/ $\sqrt { 2 }$ B) h_A/h_B = 1/2 C) h_A/h_B = 1/4 D) h_A/h_B = 1/8

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Quizplus · Accepted Answer

The time taken by an object to reach the ground from a height h is given by t= sqrt(2h/g), where g is the acceleration due to gravity. As the two objects are identical, their g is the same. Let the height from which A and B are dropped be hA and hB respectively. According to the problem, it takes twice as long for B to reach the ground as it takes for A. Therefore, tB = 2tA, or sqrt(2hB/g) = 2sqrt(2hA/g). After squaring both sides, we get hB = 4hA, or hA/hB = 1/4. Therefore, the ratio of the heights from which A and B fell is 1/4. Hence, the correct answer is option C.

Two Identical Objects a and B Fall from Rest from Different