SOLUTION: 1) The Path of a falling object is given by the function s=-16t^2+v^o t+s^o where v^o represents the initial velocity in ft/sec and s^o represents the initial height in feet. A)

Algebra ->  Algebra  -> Square-cubic-other-roots -> SOLUTION: 1) The Path of a falling object is given by the function s=-16t^2+v^o t+s^o where v^o represents the initial velocity in ft/sec and s^o represents the initial height in feet. A)      Log On

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Question 161504: 1) The Path of a falling object is given by the function s=-16t^2+v^o t+s^o where v^o represents the initial velocity in ft/sec and s^o represents the initial height in feet.
A) If a rock is thrown upward what an initial velocity of 64 feet per second from the top of a 25-foot building, write the height (S) equation using this information.
I got s=-16t^2+64t+25
B) How high is the rock after 1 second?
I got s=-16*1^2+64*1+25 so s=73
The questions I need the help on is C)& D)
C) After how many seconds will the graph reach maximum height?
D) What is the maximim height?

Answer by jim_thompson5910(21685) About Me  (Show Source):
You can put this solution on YOUR website!
Note: I'm replacing "s" with "y" and "t" with "x" to get the equation y=-16x%5E2%2B64x%2B25

To answers questions C and D, we need to find the vertex. Remember, the vertex represents the highest/lowest point.



In order to find the vertex, we first need to find the x-coordinate of the vertex.


To find the x-coordinate of the vertex, use this formula: x=%28-b%29%2F%282a%29.


x=%28-b%29%2F%282a%29 Start with the given formula.


From y=-16x%5E2%2B64x%2B25, we can see that a=-16, b=64, and c=25.


x=%28-%2864%29%29%2F%282%28-16%29%29 Plug in a=-16 and b=64.


x=%28-64%29%2F%28-32%29 Multiply 2 and -16 to get -32.


x=2 Divide.


So the x-coordinate of the vertex is x=2. Note: this means that the axis of symmetry is also x=2.


Now that we know the x-coordinate of the vertex, we can use it to find the y-coordinate of the vertex.


y=-16x%5E2%2B64x%2B25 Start with the given equation.


y=-16%282%29%5E2%2B64%282%29%2B25 Plug in x=2.


y=-16%284%29%2B64%282%29%2B25 Square 2 to get 4.


y=-64%2B64%282%29%2B25 Multiply -16 and 4 to get -64.


y=-64%2B128%2B25 Multiply 64 and 2 to get 128.


y=89 Combine like terms.


So the y-coordinate of the vertex is y=89.


So the vertex is .


Since the vertex is , this means that x=2 and y=89.


So at 2 seconds, the object is at the highest point of 89 feet.