Answer
(a) $23.32\ ft/sec$
(b) $12.88\ ft$
Work Step by Step
(a) Use the given formula $y=\frac{-16x^2}{0.434v^2}+1.15x+8$ with $x=15, y=10$, we have $10=\frac{-16(15)^2}{0.434v^2}+1.15(15)+8$ which gives $v\approx23.32\ ft/sec$ (discard negative answer)
(b) Let $a=\frac{-16}{0.434v^2}, b=1.15$, the maximum height happens when $x=-\frac{b}{2a}\approx8.48\ sec$ and the maximum height is $y=\frac{-16(8.48)^2}{0.434(23.32)^2}+1.15(8.48)+8\approx12.88\ ft$
