Constant Acceleration one dimension

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Homework Help Overview

The discussion revolves around a problem involving a rocket's motion under constant acceleration, specifically focusing on its height, velocity, and time of flight during ascent and descent. The subject area includes kinematics and the effects of gravity on motion.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to apply kinematic equations to determine the rocket's height and velocity at various stages of its flight. Some participants question the initial conditions, particularly the initial velocity and the effect of gravity after fuel depletion. Others suggest recalculating the displacement from the point of fuel exhaustion and considering the total time of flight.

Discussion Status

Participants are actively engaging with the problem, offering guidance on how to approach the kinematics after the rocket runs out of fuel. There is a recognition of the need to account for the rocket's initial velocity and elevation when calculating its maximum height and descent time. Multiple interpretations of the problem are being explored, particularly regarding the effects of gravity and the total time of flight.

Contextual Notes

There is a mention of the rocket's initial conditions, including its acceleration and the time it accelerates before running out of fuel. The discussion also highlights the need to consider the effects of gravity after fuel depletion, as well as the total time taken for the rocket's ascent and descent.

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Homework Statement


A rocket starting at rest takes on a net acceleration of 20m/s^2 in a vertical line until it runs out of fuel after 5 seconds.

At what height does it run out of fuel?
What is its velocity when it runs out of fuel?
What is its maximum height?
How long does it take to hit the ground?

Homework Equations


g = -10m/s^2

The Attempt at a Solution


x(t) = 1/2at^2 + volt

Vo = 0
a = 20m/s^2
t = 5

a)10(25) m = 250m
b)v(t) = at + vo
v(t) = (20)(5) = 100 m/s

c) max height
v(t) = 0
at + vo = 0
at = 0
*;/

d) x(t) = 0
1/2at^2 + volt
5t^2 + 0What did I do wrong :/. The net acceleration part is confusing me. Is the Vo zero?
 
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You need to do more kinematics starting at the point when the rocket runs out of fuel. Now your only acceleration is gravity, and you've got the rocket's velocity at this point and its elevation. Find its displacement from this point of reference.
 
physicsface said:
You need to do more kinematics starting at the point when the rocket runs out of fuel. Now your only acceleration is gravity, and you've got the rocket's velocity at this point and its elevation. Find its displacement from this point of reference.

Hm,
So...
c)
Vo = 100m/s

v(t) = -10t + 100m/s
0
-100/-10 = t
t = 10 s
x(10) = -500 + 1000
= 500m
d) = 20 s?
 
c) You forgot about the elevation it was already at! The rocket's at 500 m displacement from the reference point at 250 m, so what's the elevation at the peak?

d) You need to include the 5 seconds it takes to run out of fuel as well as the time it takes to get through the last 250 m of its fall.
 

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