At the initial moment three points A, B and C are on a horizontal straight line at equal distances from one another. Point A begins to move vertically upward with a constant velocity and point C vertically downward without any initial velocity but with a constant acceleration a. How should point B move vertically for all the three points to be constantly on one straight line. The points begin to move simultaneously.

Question

At the initial moment three points A, B and C are on a horizontal straight line at equal distances from one another. Point A begins to move vertically upward with a constant velocity and point C vertically downward without any initial velocity but with a constant acceleration a. How should point B move vertically for all the three points to be constantly on one straight line. The points begin to move simultaneously.

Infinity Learn · Accepted Answer

Let $$AB=BC=dBD=xand$$ BB'$$=s=$$ displacement of point B.From similar triangles we can write,$$vtd+x=sx=12at2d-xFrom$$ first two equations we have,$$1+dx=vts$$ or $$dx=vts-1$$.....(i)From$$ last two equations we have,$$dx-1=12at2s$$ $$dx=12at2s+1$$.....$$(ii)Equating$$ Eqs. $$(i) and (ii), we $$havevts-1=12at2s+1orvt-12at2s=2$$ ∴$$s=v2t-12a2t2Comparing$$ with $$s=ut+12at2$$ we have, Initial velocity of B is $$+v2$$ and acceleration $$-a2$$

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