SOLUTION: A toy rocket is launched from the top of a building 114 feet tall at an initial velocity of 167 feet per second a) give the function that describes the height of the rocket in ter

Question 1157115: A toy rocket is launched from the top of a building 114 feet tall at an initial velocity of 167 feet per second
a) give the function that describes the height of the rocket in terms of time t
b) determine the time at which the rocket reaches its maximum height, and the maximum height in feet
c) for what time interval will the rocket be more than 122 feet above ground level
d) after ho many seconds will it hit the ground?
the function that describes the height of the rocket in terms of t is s(t)=
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
The function is f(t)= -16t^2+167t+114, the first for acceleration due to gravity, the second for initial speed, the third for initial height.
maximum height t is -b/2a or -167/-32-5.22 sec
height is 549.76 feet using 5.22.
set the equation = to 122
then it becomes -16t^2+167t-8=0
t=(-167+/- sqrt (167^2-512)/-32; sqrt term is 27377 and that equals+/- 165.46
t=-1.54/-32 or 0.048 sec
t=-332.46/-32 or 10.39 sec
That interval is 10.34 sec (rounded)
hits the ground when original equation equals 0.
t=(-167+/- sqrt (35185))/-32; -167+/-187.58=-354.58
divide by -32 and
t=11.08 sec

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