SUVAT help
z = z0 + v0*t + 1/2*a*t2
dz/dt = v = v0 + a*t
v0 = 10 m/s
a = 1.6 m/s2
z0 = 0
zsurface = 120 m
120 = 10*t + 1/2*1.6*t2
0 = -120 + 10*t + 0.8*t2 (quadratic equation)
a = 0.8, b = 10, c = -120
t = (-b +/- [b2 - 4*a*c]1/2)/2*a
t = (-10 +/- [102 - 4*0.8*(-120)]1/2)/2*(0.8)
t = (7.5, -20) (can't have negative time so t = 7.5s)
vsurface = 10 + 1.6(7.5) = 22 s
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of course using your equation
(vsurface)2 = (v0)2 + 2*a*z
v0 = 10 m/s
a = 1.6 m/s2
z = 120m
v_surface = (100 + 2*1.6*120)1/2 = 22 s
if down is positive, that means your at 120 m when you hit the surface. That is why down should be negative so you are at zero when you hit the surface.
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