Question #190575

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 .


1
Expert's answer
2021-05-08T14:39:21-0400

tup=ug, sup=u22g,t_{up}=\frac ug,~s_{up}=\frac{u^2}{2g},

s=sups=u22gu(ugt)+gt22=utu22g+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},

v=ug(ugt)=gt,v'=u-g(\frac ug-t)=gt,

gttgt22=sgt22,gtt'-\frac{gt'^2}{2}=s-\frac{gt'^2}{2},

t=sgt=ugt2,t'=\frac{s}{gt}=\frac ug-\frac t2,

T=t+t=t2+ug.T=t+t'=\frac t2+\frac ug.


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