help me with this please

Question

Use the formula h = −16t² + v₀t

 discussed in Example 7.

How fast would a ball have to be thrown upward to reach a maximum height of 144 ft? [Hint: Use the discriminant of the equation 16t² − v₀t + h = 0.]

Answer 1

-16t^2 + vot = h

h' = v = -32t + vo = 0

t = vo/32 when h = max

plug that into the h equation to get

144 = -16(vo/32)^2 + vo(vo/32) = - vo^2/64 + vo^2/32 = vo^2/64

vo^2 = 64(144)

vo = 8(12) = 96 feet per second = initial velocity to reach max height of 144 feet