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Part $1$

A ball is thrown directly upward from a height of

$77$

ft with an initial velocity of

$2424$

$$ft$/$sec$.$ The function

$$s$($t$)$equals$=$negative $16$ t squared plus $24$ t plus $716$t$2+24$t$+7$

gives the height of the$$ ball, in$$ feet, t seconds after it has been thrown. Determine the time at which the ball reaches its maximum height and find the maximum height.