If a stone is dropped from a height of 576 feet, its height s after t seconds is
ID: 2889261 • Letter: I
Question
If a stone is dropped from a height of 576 feet, its height s after t seconds is given by s(t) = 576 16t2, with s in feet.
(a) Compute
s'(t).= _________
Find its velocity at times t = 0, 1, 2, 3, and 4 seconds.
s'(0) =
s'(1) =
s'(2) =
s'(3) =
s'(4) =
(b) When does it reach the ground, and how fast is it traveling when it hits the ground? HINT [It reaches the ground when s(t) = 0.]
The stone is traveling at a velocity of ______ ft/sec when it hits the ground at ________seconds.
s'(0) =
_____ ft/secs'(1) =
_____ft/secs'(2) =
______ft/secs'(3) =
______ft/secs'(4) =
______ft/secExplanation / Answer
s=576-16t2
s'(t) = -2(16t)= -32tft/s
s'(0)=-2(0)=0
s'(1)=-32(1)=-32ft/s
s'(2)=-32(2)=-64ft/s
s'(3)=-32(3)=-96ft/s
s'(4)=-32(4)=-128ft/s
b. s(t)=0
576-16t2=0
t2=36
t=6
s'(6)=-32(6)=-192ft/s
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