SOLUTION: A model rocket is launched with and intitial velocity of 120 feet per second from a height of 20 feet. The height of the rocket t seconds after it has been launched is given by the

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Question 1008914: A model rocket is launched with and intitial velocity of 120 feet per second from a height of 20 feet. The height of the rocket t seconds after it has been launched is given by the function
s(t)=-16t^2+120t+20
question
A) After how many seconds will the rocket reach its maximum height?
B)What will be the maximum height of the rocket?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
When the equation has the form
+f%28t%29+=+a%2At%5E2+%2B+b%2At+%2B+c+, the
x-coordinate of the maximum is at
+x%5Bmax%5D+=+-b%2F%282a%29+
+a+=+-16+
+b+=+120+
--------------
(A)
+x%5Bmax%5D+=+-120%2F%282%2A%28-16%29%29+
+x%5Bmax%5D+=+15%2F4+
+x%5Bmax%5D+=+3.75+ sec
(B)
+s%28t%29=+-16t%5E2+%2B+120t+%2B+20+
+s%283.75%29+=+-16%2A14.0625+%2B+120%2A3.75+%2B+20+
+s%283.75%29+=+-225+%2B+450+%2B+20+
+s%283.75%29+=+245+
The maximum height is 245 ft