Question

Im not getting the math

At maximum height, the y-component of the velocity of the rocket is zero.
That is, vy = 0 m/s
Then,
0 = v0y+βt-(γ/2)t^22
0 = (7.00 m/s)+(9.00 m/s2)t-(1.40 m/s3/2)t^2
Thus,
(0.7)t2-(9.00)t-7 = 0
Solving the above quadratic equation, we get
t = 13.59 s

where does the 0.7 come from?

Answer 1

it looks like in the squared term
(γ/2)t^2

γ is 1.40. They plug in Y to get
(1.40 m/s3/2)t^2
buried in that expression is the divide by 2 (lost among the units!)
you get 0.7 t^2

Answer 2

ohhh tyy