An angry construction worker throws his wrench downward from

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)__16t2 _ 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?

Solution

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)__16t2 _ 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?
.
S(t) = -16t^2 + 32t + 128
a) What is the height of the wrench after 1 second?
S(t) = -16t^2 + 32t + 128
S(1) = -16(1)^2 + 32(1) + 128
S(1) = -16 + 32 + 128
S(1) = 16 + 128
S(1) = 144 feet
.
b) How long does it take for the wrench to reach the
ground?
Set S(t) = 0 and solve for t
S(t) = -16t^2 + 32t + 128
0 = -16t^2 + 32t + 128
Dividing both sides by -16:
0 = t^2 - 2t - 8
0 = (t-4)(t+2)
t = {-2,4}
We can throw out the negative solution leaving:
t = 4 seconds