SOLUTION: Throwing a wrench. An angry construction 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 abo
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-> SOLUTION: Throwing a wrench. An angry construction 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 abo
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Question 358880: Throwing a wrench. An angry construction 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 1 second?
b) How long does it take for the wrench to reach the
ground?
You can put this solution on YOUR website! 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 1 second?
S(t) = the height, t=1; therefore:
S(t) = -16(1^2 - 32(1) + 128
S(t) = -16 - 32 + 128
S(t) = 80 ft after one second
:
b) How long does it take for the wrench to reach the ground?
Replace height [S(t)] with ground level, which is 0
-16t^2 - 32t + 128 = 0
Simplify and change the signs, divide equation by -16
t^2 + 2t - 8 = 0
Factor
(t+4)(t-2) = 0
The positive solution is all we want here
t = 2 seconds for the wrench to reach the ground
:
:
We can prove this:
S(t) = -16(2^2) - 32(2) + 128
S(t) = -16(4) - 64 + 128
S(t) = -64 - 64 + 128
S(t) = 0
:
:
Did this make sense to you now?
