How Long Does It Take for a Rocket to Return After Stopping Its Initial Ascent?

[Physicsnoob90]

Homework Statement

A model rocket takes off from ground level accelerating upward at a = 3.0 g. This upward acceleration lasts for a time τ = 15 s. Afterward the rocket continues upward, eventually stops rising, then falls back to the ground.
How much time passes from the initial upward acceleration stopping to the rocket returning to the ground?

Homework Equations

constant acceleration

The Attempt at a Solution

i broke them down to two different moments (1. during the blast off, 2. when it comes back down.)

moment 1: let t = τ , vf = aτ , ∆y = 1/2 aτ^2

moment 2 : 1) ∆y = vot + 1/2at^2
aτ^2 = aτ - 1/2gt^2

 

[SteamKing]

Homework Statement

A model rocket takes off from ground level accelerating upward at a = 3.0 g. This upward acceleration lasts for a time τ = 15 s. Afterward the rocket continues upward, eventually stops rising, then falls back to the ground.
How much time passes from the initial upward acceleration stopping to the rocket returning to the ground?

Homework Equations

constant acceleration

The Attempt at a Solution

i broke them down to two different moments (1. during the blast off, 2. when it comes back down.)

moment 1: let t = τ , vf = aτ , ∆y = 1/2 aτ^2

moment 2 : 1) ∆y = vot + 1/2at^2
aτ^2 = aτ - 1/2gt^2

And?

The "attempt at a solution" means, you know, actually working out the solution, not just throwing a few equations out at random.