Posted by Eve on Monday, September 15, 2008 at 11:39pm.
v = Vo - 9.8 t
height versus time is a parabola
h = Vo t - 4.9 t^2
Vertex is at the top where v = 0 call that height capital H
0 = Vo - 9.8 ttop
ttop = Vo/9.8
H = Vo ttop - 4.9 ttop^2
H = Vo^2/9.8 - .5 Vo^2/9.8
H = .5 (Vo^2/9.8)
H/4 = .125 (Vo^2/9.8)
at some time t it is at H/4 and v =18
v = 18 = Vo - 9.8 t
H/4 = Vo t - 4.9 t^2 = .125 Vo^2/9.8
Vo = 18 + 9.8 t
that gives two equations in the two unknowns, t and Vo
solve for Vo
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