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A ball travels on a parabolic path in which the height (in feet) is given by the expression \(-16t^2+64t+31\), where \(t\) is the time after launch. What is the maximum height of the ball, in feet?

 Jul 30, 2019

5+0 Answers

 #1
avatar+9479 
+3

h  =  -16t2 + 64t + 31

 

maximum value of  h  will occur when    t  =  -b / [2a]

 

that is, when   t  =  -64 / [ 2(-16) ]

 

Once you know the value of  t  that produces the maximum value of  h ,

plug that value in for  t  to find the height at that time.

 

Can you finish it? If you get stuck let us know.

 Jul 30, 2019
 #2
avatar
+1

I'm stuck i got t = 2 but what do I do from now.

 Jul 31, 2019
 #3
avatar+129852 
+2

Since the max height occurs at t = 2

 

Just stick 2 into the function for t   and evaluate

 

So....you are evaluating

 

-16(2)^2  + 64(2)  + 31      =   max height

 

Can you take it from here, Logic ????

 

 

 

cool cool cool

CPhill  Jul 31, 2019
 #4
avatar+1207 
+1

Thanks hectictar and CPhill I got 95 is that correct?!?

 Jul 31, 2019
 #5
avatar+9479 
+1

Yes, that is correct! smiley

 

Here's a graph of the equation   h  =  -16t2 + 64t + 31

 

where you can see that the maximum value of  h  is  95  and it occurs when  t = 2

 

https://www.desmos.com/calculator/wtrtbakdpy

hectictar  Jul 31, 2019

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