How to Calculate the Flight Time and Apex for a Model Rocket Launch in Excel?

[radarspec]

A brief explanation, this assignment is to be done in Excel and also has to be turned in with handwritten solutions for finding total flight time and apex. If I can get the handwritten part done Excel is a piece of cake.

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/s². 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/s²
F_E=16N
m=0.05 kg
v_o=0m/s
\Deltat=0.01s

Unknowns:
acceleration
velocity
height
total time

Homework Equations

\SigmaF=ma
v(t)=v_o+at
h(t)=h_o+v_o+.5at²

The Attempt at a Solution

Stage 1: 0\leq t \leq 0.15s
use dt=0.01s (was told to do this by teacher for stage 1)
\SigmaF=ma
F_e-w=may
a_y=\frac{Fe-w}{m}
a_y=\frac{16N-(0.05)(9.81)}{0.05}=310.19m/s²

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

h=h_o+v₀+.5at2
h=.5at²
h=.5(310.19)(0.15)2
h=10.47 m

Stage 2: 0.15 \leq t \leq 6.15s
\SigmaF=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 \leq t \leq total time

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

 

[D H]

Your stage 2 is incorrect. At the end of stage 1, you have the rocket's velocity as 46.53 m/s upwards (correct). Then at the end of stage 2, during which the only force is gravity (downward), you have the rocket's velocity as 106.86 m/s upwards. Ask yourself, does this make any sense?

 

[radarspec]

So I would be using -9.81 instead of 9.81 for gravity now? Also would apex be the addition of the height of stage 1 & 2 added together. 111.11 + 10.47 = 121.58m?

Also the velocity and height numbers seem small given the acceleration at lift off.