Question 161464: A worker throws his wrench downward from a height of 128 feet with an initial velocity of 32 feet per second. The height of the wrench above the ground after t seconds is given by S(t)= -16t^2-32t+128 .
a. What is the height of the wrench after one second?
b. How long does it take the wrench to reach the ground?
Thanks for the help.
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A worker throws his wrench downward from a height of 128 feet with an initial
velocity of 32 feet per second. The height of the wrench above the ground after
t seconds is given by S(t)= -16t^2-32t+128 .
:
a. What is the height of the wrench after one second?
Substitute 1 for t in the given equation:
h = -16(1^1) - 32(1) + 128
h = -16 - 32 + 128
h = 80 ft after 1 sec
:
:
b. How long does it take the wrench to reach the ground?
h = 0 when the wrench reaches the ground
-16t^2 - 32t + 128 = 0
:
Simplify this, divide equation by -16, results:
+t^2 + 2t - 8 = 0
:
Factor this to:
(t+4)(t-2) = 0
:
The positive solution is what we want here.
t = 2 sec to reach the ground
:
:
Check solution in original equation for t=2:
-16(2^2) - 32(2) + 128
-64 - 64 + 128 = 0
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