SOLUTION: A model rocket is projected straight upward from the ground level according to the height equation h= -16t^2+192t, where t is greater than or = to 0. What is the maxi

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Question 286500: A model rocket is projected straight upward from the ground level according to the height equation h= -16t^2+192t, where t is greater than or = to 0. What is the maximum height of the rocket and after how many seconds does the rocket reach maximum height?
I am just somewhat frustrated because it seems as thought the book and my lecture do not have sufficient information to answer this question, and I could really use some help. Thanks.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Note: I'm using 'x' instead of 't' and 'y' instead of 'h'


The max height will occur at the vertex since the vertex is the highest/lowest point on the parabola. So we must find the vertex.


To find the vertex, we'll use the formula x=-b%2F2a which is the x coordinate of the vertex. Since y=-16x%5E2%2B192x is in the form y=ax%5E2%2Bbx%2Bc where a=-16, b=192 and c=0, we can plug these values in x=-b%2F2a to get x=-b%2F2a=-192%2F%282%28-16%29%29=-192%2F%28-32%29=6


So the 'x' coordinate of the vertex is x=6. So the highest point occurs when x=6 or equivalently when t=6 (since I replaced 't' with 'x'). So the rocket reaches the max height at 6 seconds.


From here, just plug t=6 into h=-16t%5E2%2B192t to find the height 'h' at that given 't' value.

Note: the vertex will be (6, h) where 'h' is the height at 6 seconds, but you probably don't need this info.