Given: at time = 0, v0=+320 ft/s, [ assumed a=-g=-32.2 on earth ]
use kinematic equation for vertical projectiles,
Height,
H(t) = 1538 = v0(t)+(1/2)at^2=320t+(1/2)(32.2)t^2
Solve for t using the quadratic formula,
with A=16.1, B=320, C=-1538:
16.1t^2+320t-1538=0
t=8.14 or t=11.74
This means that at t=8.14, the projectile reaches 1538 feet (on its way up), and at t=11.74, the projectile falls back down and reaches also 1538 feet.
