Topic 2 Examples


 * 1) Two identical objects A and B fall from rest from different heights. If B takes twice as long as A to reach the ground, what is the ratio of the heights from which A and B fell? Neglect air resistance.
 * A  1: 2^(1/2)          B  1:2         C  1:4        D  1:8
 * To answer this question, we must first understand two things: a ratio is a fraction, and we must know our variables. In the question we are given the time (t for A and 2t for B), the heights (Ha & Hb), the initial velocity (v=0), and we know acceleration due to gravity to be g. We can look at these variables and recognize that they are all in the kinematic equation: H = vt + (1/2)at^2. We can now substitute the variables we know into two equations: one for A and one for B. When we do this, we get: Ha = (1/2)gt^2 and Hb = (1/2)g(2t)^2 = 2gt^2. We can now solve for g in both equations because we know it is a constant, and we can set the two equal. After this we derive g = (2Ha)/(t^2) = (Hb)/(2t^2) = g. In order to find our final answer, we now create a fraction in the form of (Ha)/(Hb) = x/y. When we solve this, we conclude that (Ha)/(Hb) = 1/4, so the answer to the question is C  1:4.

