An object is vertically projected at u velocity ..After t time another one is projected at the same velocity. Show the meeting time is (t/2 + u/g) after the first object projected .
tup=ug, sup=u22g,t_{up}=\frac ug,~s_{up}=\frac{u^2}{2g},tup=gu, sup=2gu2,
s=sup−s′=u22g−u(ug−t)+gt22=ut−u22g+gt22,s=s_{up}-s'=\frac{u^2}{2g}-u(\frac ug-t)+\frac{gt^2}{2}=ut-\frac{u^2}{2g}+\frac{gt^2}{2},s=sup−s′=2gu2−u(gu−t)+2gt2=ut−2gu2+2gt2,
v′=u−g(ug−t)=gt,v'=u-g(\frac ug-t)=gt,v′=u−g(gu−t)=gt,
gtt′−gt′22=s−gt′22,gtt'-\frac{gt'^2}{2}=s-\frac{gt'^2}{2},gtt′−2gt′2=s−2gt′2,
t′=sgt=ug−t2,t'=\frac{s}{gt}=\frac ug-\frac t2,t′=gts=gu−2t,
T=t+t′=t2+ug.T=t+t'=\frac t2+\frac ug.T=t+t′=2t+gu.
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