# A rocket physics question

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1. Oct 5, 2015

### GZM

1. The problem statement, all variables and given/known data
Problem : During your summer internship for an aerospace company, you are asked to design a small research rocket. The rocket is to be launched from rest from the earth's surface and is to reach a maximum height of 990 m above the earth's surface. The rocket's engines give the rocket an upward acceleration of 16.0 m/s2 during the time T that they fire. After the engines shut off, the rocket is in free fall. Ignore air resistance.

What it asks for : What must be the value of T in order for the rocket to reach the required altitude?

2. Relevant equations
Kinematic equations : d=vi*t+(1/2)*a*t^2
vf^2 = vi ^2 + 2*a*d
vf = vi + at

3. The attempt at a solution
My attempt at the solution was that i thought at the apex of the height 990 m the final velocity would be 0,
since they give us acceleration, distance and I can guess that vf is zero
Step 1 ) i used the equation vf = vi+at, i would solve for t and it would be t = -Vi/16
Step 2 ) i would use vf^2 = vi^2 + 2ad but when I isolate Vi it would become negative and I can't square root, so

2. Oct 5, 2015

### SteamKing

Staff Emeritus
This problem is a little different from most projectile problems, in that at launch, the rocket's velocity is zero and when the rocket reaches its maximum altitude, its velocity is also zero.

The acceleration of 16 m/s2 need not be applied during the entire duration of the upward flight in order for the rocket to reach an altitude of 990 m. After the rocket motor shuts off, the rocket will continue to travel upward until gravity reduces its ascent velocity to zero, after which the rocket free falls back to earth.

3. Oct 5, 2015

### GZM

Oh, i got the whole concept wrong, so how would I set up this equation I did something like this, would this be somewhat appropriate,

4. Oct 5, 2015

### CWatters

You need two equations, one for each phase.

5. Oct 5, 2015

### GZM

Hi, thanks for responding so you say I need two equations for each phase so i assume my diagram is correct, could you give me an idea which equations I could possibly use and equate to each other to solve for T?

6. Oct 5, 2015

### SteamKing

Staff Emeritus
I don't understand stream of consciousness type of writing. It indicates a lack of focus and the clarity needed for analysis of a problem.

You know that there will be two phases to the rocket's flight:
1. Rocket takes off, flies upward a certain distance d1 while accelerating at 16 m/s2
2. When the rocket reaches d1, it stops accelerating and its velocity carries upward a further distance d2 until its velocity reaches 0.

Obviously, d1 + d2 must equal 990 m.

Write an equation for each phase of the flight.

7. Oct 5, 2015

### GZM

I am so sorry if I seem like I don't really care, but I do I am just very confused and really tired plus these things don't come naturally to me :[ that is why I am seeking help, so I really appreciate you helping me!

Now with what you have helped me with me I have discovered these equations and I substituted them in do you think I have done it correctly? :D ( the V2 comes from the diagram I had earlier is it still a right approach to the problem?

8. Oct 5, 2015

### SteamKing

Staff Emeritus
Looks good. I get your time for the duration the rocket motor is on.

9. Oct 5, 2015

### GZM

Haha thanks I really appreciate the help, new to the forum but I love it so much already, you guys here really help guide me through without actually giving me the answer just what I needed XD

10. Oct 6, 2015

### azizlwl

Should sketch velocity versus time graph and deduce equations. Let V be the final velocity from first leg.