A ball is dropped from rest from the top of a building and strikes the ground wi

Question

A ball is dropped from rest from the top of a building and strikes the ground with speed v sub f. From ground level, a second ball is thrown straight upward at the same instant that the first ball is dropped. The initial speed of the second ball is v sub o equals v sub f, the same speed at which the ball will eventually strike the ground. Ignoring air resistance, decide whether the balls cross paths at half the height of the building, above the halfway point, or below the halfway point. Give reasoning.

Explanation / Answer

h = height of the building A ball is dropped from rest from the top of a building and strikes the ground with speed v sub f. so v sub f = vf = sqrt(2gh) From ground level, a second ball is thrown straight upward at the same instant that the first ball is dropped. The initial speed of the second ball is v sub o equals v sub f, the same speed at which the ball will eventually strike the ground. so v sub 0 = v0 = sqrt(2gh) after time t, they cross paths the 1st ball at the height y = h - gt^2/2 the 2nd ball at the height y = v0t - gt^2/2 so h - gt^2/2 = v0t - gt^2/2 t = h/v0 = sqrt[h/(2g)] y = h - g*h/(2g)/2 = 3h/4 So the balls cross paths at above the halfway point.

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