The equation for the motion of a projectile fired straight up at an initial velocity of 64 ft/s is h = 64t - 16t2, where h is the height in feet and t is the time in seconds. find the time the projectile needs to reach its highest point. how high will it go?

The projectile will reach its highest point when its velocity is zero. 
According to equation:
h = 64t - 16t² 

Differentiating it with respect to t we get the velocity. 
dh/dt = v = 64 - 32t 

For max. h, v must be zero. 
therefore t = 64/32
                  = 2sec 
putting it in h = 64t - 16t² 
we get
h=64(2)-16(2)²
  =64 ft 

So time = 2sec 
and height = 64 ft