# Algebra

A catapult launches a boulder with an upward velocity of 92 ft/s. The height of the boulder, h, in feet after t seconds is given by the function h=-16t^2+92t+30. How long Does it take the boulder to reach it’s maximum height? What is the boulders maximum height

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1. the max height is on the axis of symmetry of the parabola

tmax = -b / (2 a) = -92 / (2 * -16)

find tmax , then substitute into the original equation to find hmax

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2. a. Y = yo+g*Tr = 0.
92 + (-32)Tr = 0
Tr = 2.9 s. = Rise time (time to reach max. ht.).

b. Y^2 = yo^2+2g*h = 0.
92^2+(-64)h = 0
h = 132 Ft. above launching point.
ho+h = 30+132 = 162 Ft. above gnd. = h max.

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