Posted by Math is HARD on Tuesday, November 9, 2010 at 5:33am.
If a projectile is launched from a platform 30 feet high with an initial velocity of 128 feet per second, then the height of the projectile at t seconds is given by s(t) = –16t2 + 128t + 30 feet.
(a) At what time does the projectile attain its maximum height? Show some work.
(b) What is the maximum height attained by the projectile? Show some work.

math  Damon, Tuesday, November 9, 2010 at 6:19am
s(t) = –16t^2 + 128t + 30
can do this with or without calculus
using calculus
ds/dt = 32 t + 128
= 0 at max height
32 t = 128
t = 4 seconds
for max height
s(4) = 16(16) +128(4) + 30
s(4) = 286
without calculus find vertex of parabola
16 t^2 128 t = s+30
complete square
t^2  8t = (1/16)s + (30/16)
t^2  8 t + 16 = (1/16)s + 15/8 + 16
(t4)^2 = etc
so vertex at t = 4