What is the ideal value of T for the rocket to reach 990 m altitude?

[GZM]

Homework Statement

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?

Homework Equations

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

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
I am stuck at this step, please help

 

[SteamKing]

Homework Statement

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?

Homework Equations

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

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
I am stuck at this step, please help

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.

 

[GZM]

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.

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,

 

[CWatters]

You need two equations, one for each phase.

 

[GZM]

You need two equations, one for each phase.

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?

 

[SteamKing]

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, View attachment 89798

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.

 

[GZM]

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.

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?

 

[SteamKing]

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

 

[GZM]

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

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

 

[azizlwl]

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