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Question

This is for algebra 11, and i am confused

You hit a ball from 4 ft above the ground with an initial vertical velocity of v ft/s. The function h = −16t2 + vt + 4 models the height h in feet of the ball at time t in seconds. Find the initial velocity for which the ball reaches a maximum height of 40 ft.

Answer 1

max h = 40

max h occurs when h' = -32t +v=0, t = v/32

40 = -16(v/32)^2 + v(v/32) +4 = v^2/32 - v^2/64 +4

36 = v^2/64

v^2 = 36(64)

v = 6(8) = 48 feet per second = initial velocity upwards vertically