A projectile is shot with a vertical velocity of v = 83 m/s. Its height at t seconds is given by s = vt + ½gt

A projectile is shot with a vertical velocity of v = 83 m/s. Its height at t seconds is given
by s = vt + ½gt2 . The value of g is -9.8 m/s2. Determine the time when the altitude is
(a) 345 m (b) 397 m (c) 0 m.

s = 83t - 4.9t^2
a) 345 = 83t - 4.9t^2
4.9t^2 -83t + 345 = 0 Use the quadratic formula
t = 7.3 and 9.6 seconds
b) 9t^2 - 83t + 397 = 0
there are no real roots because 397 is above the max height of the projectile
dS/dt = 83 - 9.8t = 0 so t = 8.46 and max height is 351m
c) 0 = 83t - 4.9t^2 = t(83-4.9t)
t = 0 and 16.94s