MATH SOLVE

6 months ago

Q:
# 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

A:

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 ⇒ -32t + 109 = 0⇒t = [tex]\frac{109}{32}[/tex] ⇒ 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) = -16×[tex]3.4^{2}[/tex] + 109×3.4 ⇒ h = 185.6ft