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September 17, 2014

September 17, 2014

Posted by **chris** on Wednesday, November 30, 2011 at 10:42pm.

h(t)=-16t^2 + 64t +80

during what time is the stone rising?

when is the stone falling?

what is the maximum upward velocity?

when does it reach its maximum height above the ground?

- calc -
**Reiny**, Wednesday, November 30, 2011 at 10:50pmh '(t) = -32t + 64

the stone is rising when h '(t) is positive

-32t + 64 ≥ 0

-32t > -64

t < 2

similarly the stone is falling for t > 2

the velocity is -32t + 64

clearly the max upwards velocity occurs when t=0 (at the beginning)

and it is 0 + 64 or 64 ft/sec

max height is when -32t + 64 = 0

t = 2

so h(2) = -64 + 128 + 80

= 144 ft

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