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## Homework Statement

A model rocket is launched and I am to evaluate the 3 stages it goes through. During the first 0.15s the rocket (m=0.05 kg) is launched with a force of 16N. It then coasts upward while being slowed done by gravity (g=9.81m/s

^{2}. After it reaches apex(max altitude it starts to fall back down. It also deploys a parachute 6 sec. after the motor stops with a constant speed of 10 m/s until it hits ground. Calculate the speed and altitude of the rocket over it's flight time and plot them.

__Knowns:__

g=9.81m/s

^{2}

F

_{E}=16N

m=0.05 kg

v

_{o}=0m/s

[tex]\Delta[/tex]t=0.01s

__Unknowns:__

acceleration

velocity

height

total time

## Homework Equations

[tex]\Sigma[/tex]F=ma

v(t)=v

_{o}+at

h(t)=h

_{o}+v

_{o}+.5at

^{2}

## The Attempt at a Solution

__Stage 1: 0[tex]\leq[/tex] t [tex]\leq[/tex] 0.15s__

use dt=0.01s (was told to do this by teacher for stage 1)

[tex]\Sigma[/tex]F=ma

F

_{e}-w=may

a

_{y}=[tex]\frac{Fe-w}{m}[/tex]

a

_{y}=[tex]\frac{16N-(0.05)(9.81)}{0.05}[/tex]=310.19m/s

^{2}

v=v

_{o}+at

v=0+(310.19)(0.15)=46.53m/s

h=h

_{o}+v

_{0}+.5at2

h=.5at

^{2}

h=.5(310.19)(0.15)2

h=10.47 m

__Stage 2: 0.15 [tex]\leq[/tex] t [tex]\leq[/tex] 6.15s__

[tex]\Sigma[/tex]F=ma

-w=ma

_{y}

a

_{y}=-g

v=v

_{o}+at

v=46.53+(9.81)(6.15)=106.86m/s

h=10.47m+(46.53)(6.15)+.5(-9.81)(6.15)

^{2}=111.11m

__Stage 3: 6.15 [tex]\leq[/tex] t [tex]\leq[/tex] total time__

Stage 3 is were I get lost could some point me in the right direction as to find total time and apex.