Rocket Launch: Solving for Height and Time

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Homework Help Overview

The problem involves a rocket launched vertically with an initial acceleration of 10 m/s² for 20 seconds before the motors are turned off. Participants are tasked with determining the maximum height reached and the total time to reach that height, considering gravitational acceleration after the motors stop.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to calculate the initial velocity and height using equations of motion but expresses uncertainty about the total time and the final velocity of the rocket. Some participants question the use of gravitational acceleration during the initial acceleration phase and clarify that it should only apply after the motors are off.

Discussion Status

Participants are actively engaging with the problem, with some providing clarifications on the physics involved. There is recognition that the original poster needs to find the height reached during the powered ascent and that the rocket continues to coast after the motors stop, leading to further questions about calculating the total height and time.

Contextual Notes

There is a noted confusion regarding the application of gravitational acceleration during different phases of the rocket's flight, as well as uncertainty about how to determine when the rocket reaches its final velocity of zero.

Dinovek
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Homework Statement


A rocket is launched off and accelerates vertically up at 10 m/s 2. At 20 seconds, the motors are turned off, but the rocket keeps going up.

a) What height did it reach?
b) What was the time it needed to reach that height?

g: - 9.8 m/s2
a: 10 m/s2
final velocity: 0 m/s (Not sure).
t=20 s

Homework Equations


h= vo (t) + g(t)2/2
t=(vf-vo)/g
vo= vf-g(t)

The Attempt at a Solution


I needed to find initial velocity to find height so I did.

vo=vf-g(t)
vo= 0 m/s - (-9.8m/s2)(20)
vo= 196 m/s

Now I just substituted to find height.

h= vo(t) + (g (t)2)/2
h= 196 m/s (20s) + (-9.8 m/s2 (20) 2)/2
h=3920 m + -3920 m/
h= 3920 m - 1960 m
h= 1960 m

I really have no clue how do to even start the problem because I'm not sure what is the time total. I was thinking that after it stops accelerating, every second it decreases 1 m/s on it's acceleration so that would 10 more seconds to the total timing.

Any help would be appreciated it. Thanks.
 
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Why did you use g for acceleration during the first 20 seconds? The rocket is accelerating at +10m/s2 during the first 10 seconds.

You would use g for acceleration after the 20 seconds, since that's when the motors are off.
 


VACA said:
Why did you use g for acceleration during the first 20 seconds? The rocket is accelerating at +10m/s2 during the first 10 seconds.

You would use g for acceleration after the 20 seconds, since that's when the motors are off.
You're right, I didn't read carefully, thanks! I'm not sure how I'm going to calculate the total height. How do I know when it's going to reach final velocity of zero?
 


Dinovek said:
You're right, I didn't read carefully, thanks! I'm not sure how I'm going to calculate the total height. How do I know when it's going to reach final velocity of zero?

You first have to find the height it reaches in the first 20 seconds. Vf will not be zero after 20 seconds. After 20 seconds it is coasting (like a car when you take your foot off of the gas). It will take more time for it to reach 0 m/s (maximum height).

Try solving the coasting part on your own, and post back if you get stumped. Hint:
Vf when the motors are going will be Vo when the rocket is coasting.
 

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