Question

A stone is dropped from a height h simultaneously another stone is thrown up from the ground which reaches the height 4h.The two stones cross each other after a time.

Answer 1

$$\begin{gathered} uisthevelocitywithwhichsecondstoneisprojected. \\ {v}^2-u^2=2as \\ atheighestpointv=0 \\ s=4h \\ a=-g \\ 0-u^2=-2g4h \\ u=\sqrt{8gh} \\ lettisthetimewhentheycrosseathother. \\ inttimedis\tan cetarvelbyfirststoneis: \\ x=ut+0.5g{t}^2 \\ x=0+0.5\times 10t^2 \\ x=5t^2 \\ dis\tan cetravelledbysecondstoneis: \\ h-x=ut-5t^2 \\ h-5t^2=\sqrt{8gh}t-5t^2 \\ h=t\sqrt{8gh} \\ t=\sqrt{\frac{h}{8g}} \end{gathered}$$