If the initial velocity in item #1 is 128 feet per second, when is the object 112 feet higher?

Question

Show your solution, it is grade 9 math

Answer 1

h(t) = -16t^2 + 128t = 118

16t^2 - 128t + 118 = 0

4t^2 - 32t + 29.5 = 0

t^2 - 8t = -29.5/4

t^2 - 8t + 16 = 16 -7.375 = 8.625

t - 4 = + or - sqr(8.625)

t = 4 + or - 2.94 = 1.06 seconds to reach 118 feet, also 6.94 seconds on the way down

max height is when t = 128/32 = 4 seconds

f(4) = -16(16) + 128(4) = -256 + 512 = 256 feet = maximum height in 4 seconds