Rocket Launch Kinematics motion

[negation]

Homework Statement

You're at a mission control for a rocket launch, deiciding whether to let the launch proceed. A band of clouds 5.3km thick extends upwards from 1.9km altitude. The rocket will accelerate at 4.6ms^-2 and it isn't allowed to be out of sight for more than 30s.
Should the launch be allowed?

Homework Equations

None.

The Attempt at a Solution

Clear skies ranges from y = [0m,1900m]
Thick cloud ranges from y = [1900m,7200m]

vf^2 - vi^2 = 2a(yf - yi)
vf^2 = 2(4.6ms^-2)(1900_
vf = 132.2ms^-1

At the instantaneous moment rocket is at position y = 1900m, vf = 132.2ms^-1

From y = 1900m, vf = 132.2ms^-1 = vi

yf - yi = vit + 0.5at^2
yf - yi = 132.2ms^-1 (30s) + 0.5(4.6ms^-2)(30)^2
yf - yi = 6036m

[yf - yi] = 6036m > 5300m from t = [0s,30s]

Launch should be allowed.

 

[haruspex]

Looks right.

 

[negation]

Looks right.

How would the equation change if the acceleration of the rocket and gravity were included within the parameter? I'm curious.

 

[Curious3141]

How would the equation change if the acceleration of the rocket and gravity were included within the parameter? I'm curious.

It already is. The net acceleration after taking into account the opposing deceleration from gravity is 4.6m/s^2. Without gravity, the rocket could presumably accelerate at (4.6 + 9.8) = 14.4 m/s^2. The rocket thrust force is 14.4*M, where M is the mass of the rocket.