# Rocket Launch Kinematics motion

1. Dec 13, 2013

### negation

1. The problem statement, all variables and given/known data

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?

2. Relevant equations

None.

3. 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.

2. Dec 13, 2013

### haruspex

Looks right.

3. Dec 13, 2013

### negation

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

4. Dec 13, 2013

### Curious3141

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.