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?

Did I miss the question?

no it looks like i didn't add what is is i need help with here is what I am looking for from the above question

a)What is the height of the wrench after 1 sec
b)how long will it take the wrench to reach the ground

this is what I came up with for a) but I am unsure about it and I am not sure how to do b)

S(t)=-16t2-32t+128
S(1)=-16-32+128
S=-48+128
S=80

yes, on a.

Now on b, set s to zero, then solve for t. Notice it is a quadratic.

This what I go and now I am stuck. Can you please let me know what I need to do next or where I am going wrong

0=-16t2-32t+128
0=t2+2t+8

-16t^2 - 32t + 128

-16(t^2 + 2t - 8)
What multiplies to -8 and adds to 2
4 & -2
t^2 + 4t - 2t - 8
Group and remove commonalities
(t^2 + 4t) (-2t - 8)
t(t+4) -2(t+4)
(t+4)(t-2)
Solve each set for 0
t+4=0
t= -4

t-2=0
t=2

To find the height of the wrench after 1 second, we can substitute t = 1 into the equation S(t) = -16t^2 - 32t + 128 and solve for S(1).

a) Plug in t = 1 into the equation:
S(1) = -16(1)^2 - 32(1) + 128
S(1) = -16 - 32 + 128
S(1) = 80 feet

So, the height of the wrench after 1 second is 80 feet.

To find the time it takes for the wrench to reach the ground, we need to find the value of t when the height, S(t), reaches 0.

b) Set S(t) = 0 and solve for t:
-16t^2 - 32t + 128 = 0

We can use the quadratic formula to solve this equation, where a = -16, b = -32, and c = 128.

t = (-b ± √(b^2 - 4ac))/(2a)

t = (-(-32) ± √((-32)^2 - 4(-16)(128)))/(2(-16))
t = (32 ± √(1024 + 8192))/(-32)
t = (32 ± √9216)/(-32)

Simplifying further:
t = (32 ± 96)/(-32)

Using both the positive and negative value, we have two possible values for t. However, we are only interested in the positive value since time cannot be negative.

t = (32 + 96)/(-32)
t = 128/(-32)
t = -4

Since time cannot be negative, the time it takes for the wrench to reach the ground is 4 seconds.

Therefore, the height of the wrench after 1 second is 80 feet, and it takes 4 seconds for the wrench to reach the ground.