# Homework Help: Newton's Third Law and rocket

1. Sep 27, 2006

### needhelp83

A Saturn V rocket has a mass of 2.75 x 106 kg and exerts a force of 3.3 x 107 N on the gases it expels. Determine:
a) the initial vertical acceleration of the rocket
b) its velocity after 8 s
c) how long it takes to reach an altitude of 9500 m.
Ignore mass of gas expelled and assume g remains constant

a)Fnet=Fengine-Fgravity
Fengine=Fnet+Fgravity
Fengine=m(a+g)
a=F/m-g=(3.3*10^7 N/2.75*10^6 kg) - 9.8=2.2m/s^2

b) Not sure how to do

c) Not sure how to do

Any help?

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2. Sep 27, 2006

### Astronuc

Staff Emeritus
That helps, although in reality the mass of the propellant decreases, and at constant thrust the acceleration is continually increasing.

Back the problem at hand.

2. What is the equation for velocity (speed) as a funtion of time when acceleration is constant?

3. What is the equation for distance traveled (altitude gained) for a mass at constant acceleration?

http://hyperphysics.phy-astr.gsu.edu/hbase/mot.html#mot1

This may come in handy later - http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html

3. Sep 28, 2006

### needhelp83

b) v=v0+at
v=0 + (2.2 m/s^2)(8 s)=17.6 m/s

c)x=v0(t)+1/2at^2
y=v0(t)+1/2at^2
9500=0+.5(2.2)(t^2)
9500/1.1=t^2
t=92.9 s

Better?