SOLUTION: 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 give
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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.
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
