Question

object thrown upward from height h with initial velocity v0.... what is the maximum height reached by the object?

Answer 1

\[V _{hmax} ^{2}=V _{0} ^{2}-2g(h _{\max}-h)\]
At hmax, \[V _{hmax} ^{2}=0\] So, \[V _{0} ^{2}/2g +h=h _{\max}\]

Answer 2

since
\[v ^{2}=u ^{2}+2as\]
since final velocity will be zero v=0
intial velocity u=v
and gravity will provide acceleration but agaist the direction of motion
so a=-g
and displacement s=h
\[0=v ^{2}-2gh\]
\[h=v ^{2}/2g\]