Question 180814
S(t)= -16t^2 -32t + 128

(a) need to find S(t) when t=1

S(1)= -16(1)^2 - 32(1) + 128
S(1)= -16 -32 + 128
S(1)= 80

At t=1second the height of the wrench is 80ft

(b)if the wrench reaches the ground, then the height is 0, ...in other words it is asking you to find t when S(t)=0....you can solve this problem two ways

(Graphing Method) 
With your calculator, graph the equation...your solution will be your zeros (or x-intercepts)....notice that x-intercepts happen at t=-4 and t=2....t=-4 does not make sense so your answer should be t=2 seconds

(Algebra Method)

0 = -16t^2 - 32t +128
0 = t^2 -32t -2048
0 = (t-64)(t+32)
0 = (t-64/-16)(t + 32/-16)
0 = (t + 4)(t-2)
(t+4)=0 or (t-2)=0
t=-4 or t=2
it would not make sense of the time to be negative....so this leaves us with one answer:  the wrench reaches the ground when t=2 seconds