SOLUTION: How high is the rock after 0.5 seconds? After how many seconds will the rock reach maximum height? What is the maximum height? S(t) = -16t^2 + 32t + 40 A falling object is giv

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: How high is the rock after 0.5 seconds? After how many seconds will the rock reach maximum height? What is the maximum height? S(t) = -16t^2 + 32t + 40 A falling object is giv      Log On


   

Question 90522: How high is the rock after 0.5 seconds?
After how many seconds will the rock reach maximum height?
What is the maximum height?
S(t) = -16t^2 + 32t + 40
A falling object is given by the function "S= -16t^2 + Vot + So" where "Vo" represents the initial velocity in ft/sec and "So" represents the initial height.
A baseball is thrown upward with an initial velocity of 32 feet per second from the top of a 40-foot skyscraper
32(0.5)=16ft high after 0.5 seconds
32(40ft)= 1280seconds reaches max height
40ft is max height
is this anywhere near correct?
help

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"How high is the rock after 0.5 seconds?"

Simply plug in t=0.5 to find the height


Lets evaluate S%280.5%29

S%28t%29=-16t%5E2%2B32t%2B40 Start with the given polynomial


S%280.5%29=-16%280.5%29%5E2%2B32%280.5%29%2B40 Plug in t=0.5




S%280.5%29=-16%280.25%29%2B32%280.5%29%2B40 Raise 0.5 to the second power to get 0.25


S%280.5%29=-4%2B32%280.5%29%2B40 Multiply -16 by 0.25 to get -4


S%280.5%29=-4%2B16%2B40 Multiply 32 by 0.5 to get 16


S%280.5%29=52 Now combine like terms


So after 0.5 seconds the rock is 52 ft high

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"After how many seconds will the rock reach maximum height?"

If we graph S%28t%29+=+-16t%5E2+%2B+32t+%2B+40 as a function of x we get

+graph%28+500%2C+500%2C+-10%2C+10%2C+-10%2C+70%2C+-16x%5E2+%2B+32x+%2B+40%29+

and with a graphing calculator (or just simply by looking at the graph) we find the peak when x=1

So after 1 second, the rock has reached the max height

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"What is the maximum height?"

Simply plug in t=1 to find the max height


Lets evaluate S%281%29

S%28t%29=-16t%5E2%2B32t%2B40 Start with the given polynomial


S%281%29=-16%281%29%5E2%2B32%281%29%2B40 Plug in t=1


S%281%29=-16%281%29%2B32%281%29%2B40 Raise 1 to the second power to get 1


S%281%29=-16%2B32%281%29%2B40 Multiply 16 by 1 to get 16


S%281%29=-16%2B32%2B40 Multiply 32 by 1 to get 32


S%281%29=56 Now combine like terms


So the max height is 56 feet