How long will it take until gravity causes the rocket to stop?

[Max CR]

If a rocket is traveling upwards at 40.24 meters per second, how long will it take until gravity (9.81 m/s) causes the rocket to stop and go downards?

Also, if a rocket is traveling at 33.96 meters per second, and then its fuel runs out, and another rocket ignites immidiately after that at a speed of 36.63 meters per second, then how much will the first rocket impact the velocity of the second rocket? Will it impact it at all?

I guess these questions are similar, This is for a out of school project that I am working on regarding rocket design. I can see that calculus is needed in this problem but i am unsure how. I have only completed calculus 1 but I am a good learner

 

[Nabeshin]

There is no calculus involved in these problems...

For the first one, it is a very basic kinematics problem. Do you happen to know the basic kinematics equations for constant acceleration?

The second question, as you phrased it, doesn't make much sense... My best guess is you have one rocket traveling up, runs out of fuel, and at that instant a rocket under it ignites and you want to know if they collide?

 

[Lok]

There is no calculus involved in these problems...

For the first one, it is a very basic kinematics problem. Do you happen to know the basic kinematics equations for constant acceleration?

The second question, as you phrased it, doesn't make much sense... My best guess is you have one rocket traveling up, runs out of fuel, and at that instant a rocket under it ignites and you want to know if they collide?

Air friction is involved, a speed and pressure dependent force. Calculus very much necessary.

Btw is it a two stage rocket?

 

[rcgldr]

My guess is that the problem assumes no gravity.

For the two rocket collision case, the second rocket should be well above the first rocket and pointed downwards. However, since both rockets experience the same gravity, they are both in the same frame of reference, so gravity is not a factor for collisions.

 

[Lok]

The first question ...for a 40.3 m/s initial speed ... the time it would take to stop in gravity is 40.24/9.81= 4.10 seconds.

The second is a mystery in the problem statement... i do think there is an impact involved so...
The first brings both to a 33m/s speed then the second ignites and has a speed of 39m/s but no ideea if it is relative to the first or to the ground. If relative to the first rocket than the two speeds will just add ( to slow for any relativistic thing to kick in), if relative to the ground than the speed will be just that and the first rocket will have no impact on the seconds speed but it will have carried it halfway up.

Usually the maximum speed depends on power and cross-section. So if the second rocket is similar to the first than no speed increase should occur ( considering that the second does not drag the first one too much through the air)