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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?

Respuesta :

syed514
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

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