Rocket Launch in 3 stages

  • Thread starter radarspec
  • Start date
  • #1
2
0
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
FE=16N
m=0.05 kg
vo=0m/s
[tex]\Delta[/tex]t=0.01s

Unknowns:
acceleration
velocity
height
total time

Homework Equations


[tex]\Sigma[/tex]F=ma
v(t)=vo+at
h(t)=ho+vo+.5at2

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
Fe-w=may
ay=[tex]\frac{Fe-w}{m}[/tex]
ay=[tex]\frac{16N-(0.05)(9.81)}{0.05}[/tex]=310.19m/s2

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

h=ho+v0+.5at2
h=.5at2
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=may
ay=-g

v=vo+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.
 

Answers and Replies

  • #2
D H
Staff Emeritus
Science Advisor
Insights Author
15,415
687
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?
 
  • #3
2
0
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.
 
Last edited:

Related Threads on Rocket Launch in 3 stages

  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
1
Views
439
  • Last Post
Replies
3
Views
3K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
4
Views
16K
  • Last Post
Replies
1
Views
3K
  • Last Post
Replies
3
Views
1K
Replies
1
Views
1K
  • Last Post
Replies
1
Views
8K
Top