Expert: Sherman D. - 9/17/2004

Question
1) a ball is thrown vertically upward with an initial speed of 60 ft/s. Its height in feet t seconds later is given by h(t)= 60t - 16t^2. what is the maximum height reached by the ball?
2) calvin wants to make a gutter with a rectangular cross section by folding up strips of equal width on a long sheet of metal that is 26 cm wide. the larger the cross-sectional dimensions, the greater the capacity of the gutter. find the dimensions that will maximize the gutter's capacity.

Answer
1.)
h(t) = -16t^2 + 60t

using the formula for the maximum

t = -b/2a

t = (-(60))/(2(-16))
t = (-60)/(-32)
t = 15/8
t = 1 7/8 or you can say 1.875

Now just plug that in for "x" and you get

h(1.875) = 60(1.875) - 16(1.875)^2
h(1.875) = 112.5 - 16(3.515625)
h(1.875) = 112.5 - 56.25
h(1.875) = 56.25

So the answer is 56.25 feet is the maximum height.

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Sorry, but on the last one, i don't think i can do since i am not all that good with word problems. Sorry i could only do #1.