A ball is thrown vertically upward from the ground with an initial velocity of 109 ft/sec. Use the quadratic functionh(t) = -16t2 + 109t to find how long it will take for the ball to reach its maximum height, and then find the maximumheight. Round your answers to the nearest tenth.

Accepted Solution

Answer:Time taken by the ball to reach its maximum height is 3.4 secmaximum height reached by the ball is 185.6ftStep-by-step explanation:h(t) = -16[tex]t^{2}[/tex] + 109theight is maximum ⇔ [tex]\frac{d}{dt}[/tex](h) = 0 and [tex]\frac{d^{2} }{dt^{2} }[/tex](h) < 0[tex]\frac{d}{dt}[/tex](h) = 0 β‡’ -32t + 109 = 0β‡’t = [tex]\frac{109}{32}[/tex] β‡’ t = 3.4sec[tex]\frac{d^{2} }{dt^{2} }[/tex](h) = -32 < 0∴h(t) is maximum at t = 3.4and maximum height is h(3.4) = -16Γ—[tex]3.4^{2}[/tex] + 109Γ—3.4 β‡’ h = 185.6ft