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Question Number 149733 by peter frank last updated on 06/Aug/21

Answered by Olaf_Thorendsen last updated on 07/Aug/21

$$\tau \mathrm{is}\mathrm{the}\mathrm{time}\mathrm{since}\mathrm{the}\mathrm{beginning}$$$$\bullet \mathrm{Particule}1:$$$$x_1=-\frac{1}{2}g{\tau }^2+u\tau$$$$\bullet \mathrm{Particule}2:$$$$x_2=-\frac{1}{2}g{(\tau -t)}^2+u(\tau -t)$$$$$$$$\mathrm{The}\mathrm{two}\mathrm{particules}\mathrm{meet}\mathrm{when}{x}_1=x_2$$$$-\frac{1}{2}g{\tau }^2+u\tau =-\frac{1}{2}g{(\tau -t)}^2+u(\tau -t)$$$$-\frac{1}{2}{gt}^2+g\tau t-ut=0$$$$-\frac{1}{2}gt+g\tau -u=0$$$$\tau =\frac{u+\frac{1}{2}gt}{g}=\frac{2u+gt}{2g}$$$$h=x_1=-\frac{1}{2}g{\left(\frac{2u+gt}{2g}\right)}^2+u\frac{2u+gt}{2g}$$$$h=-\frac{4u^2+g^2{t}^2+4ugt}{8g}+\frac{8u^2+4ugt}{8g}$$$$h=\frac{4u^2-g^2{t}^2}{8g}$$

Commented by peter frank last updated on 23/Aug/21

$$\mathrm{thank}\mathrm{you}$$

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