Jessica M.

asked • 01/26/16

Can someone please answer and explain this to me?

A baseball is hit during a high school tournament. The function h=-4t+16t+0.5 describes its path, where h is height in metres and t is time in seconds from the instant the ball is hit. Algebraically determine the maximum height the ball reaches. 

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Shada S. answered • 01/26/16

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First, are you sure that you have typed the equation correctly? Double check it please. My other question is, have you studied about derivatives and maximum and minimum of functions?  
 
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Jessica M.

I did mess up on the equation, sorry. It was supposed to be h= -4t^2 +16t + 0.5  I just forgot the square. And derivatives, no. Maximum and minimum yes.
 
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01/26/16

Shada S.

OK. Then we have the quadratic function h(t) = -4 t2 + 16 t + 0.5
                                                           h(t)  =  a t2  + b t   + c   ( general form of a quadratic function)
 
If you have studied about the maximum and minimum of a quadratic function, then the maximum of h(t) (by definition) will occur at  t = - b/(2a), in our case, a = -4 and b = 16
 
 So the maximum height will occur at time t = - 16/ (2*-4) = -16/ -8 = 2 seconds
 
 So we need to find the height at t = 2 seconds and that will be the maximum height
 
 h(2) = -4 *(2)^2 + 16*(2) + 0.5 =16.5 m
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01/26/16

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