Velocity Problem help!!! PLEASE!!

[tedog1985]

If a cannonball is shot directy upward with an initial velocity of 256 ft per second, its height abouve the ground after t seconds is given by

s(t) = 256t - 16t^2

A. Find the velocity and acceleration after t seconds?


B. What is the maximum height the cannonball reaches?



C. At what time t does the cannonball hit the ground?



Please help im lost on how to do this!!

 

[Razor X]

A.

v(t) = s'(t) = 256 - 32t

B.

Crit. values of s(t) when

v(c) = 0
c = 8

Loc. Max. of s(t) if s''(c) < 0

s''(t) = -32
s''(8) = -32 < 0

therefore when t = 8, s(t) is at a maximum.

C.

Canonball hits ground when

s(t) = 0
t = 0 or t = 16

at t = 0 the Cannonball has not been fired yet, therefore at t = 16 the Cannonball has hit the ground.