A ball is thrown upward with an initial velocity v0. When it is halfway to its highest point, what is its
velocity in terms of v0?
So – lets define upward as positive, and set the maximum vertical displacement as ΔyMAX. So then,

 ΔyMAX
when the ball is halfway to the apex of flight… Δy =
. From our three equations for objects
2
 
under constant acceleration… vF2 = vO2 + 2 g • Δy , and then when the vector directions are taken into
vo2
2
2
account… vF = vO − 2gΔy , and at the maximum height the final velocity is zero. Thus, ΔyMAX =
2g
2
2
2
v 
v 
v 
v
So, when halfway to the top vF2 = vO2 − 2g  o  and then vF2 = vO2 −  O  → vF2 =  O  → vF = O
2
 4g 
2
2