Rocket Acceleration Calculation

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Homework Help Overview

The problem involves calculating the acceleration of a rocket during its initial launch phase. The rocket, weighing 1000 kg, experiences a net constant upward acceleration for 16 seconds before the motor shuts off. After an additional 4 seconds, the rocket reaches an altitude of 5100 meters, prompting questions about the acceleration during the first phase of flight.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the calculations related to the rocket's velocity and height, questioning the assumptions about the rocket's state at 5100 meters. There are attempts to express the relationship between acceleration, velocity, and height using equations of motion.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and the relationships between the variables involved. Some have suggested equations to relate acceleration to the rocket's height and velocity, while others are clarifying the conditions stated in the assignment.

Contextual Notes

There is a noted ambiguity regarding the rocket's state at the altitude of 5100 meters, as the assignment does not specify whether the rocket is at rest or still in motion at that point. Additionally, the relevance of the rocket's mass is questioned in the context of the calculations being discussed.

jenduncan
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A 1000 kg rocket is launched straight up. The rocket motor overcomes gravity to provide the rocket with a net constant acceleration upward for 16 seconds. The the motor shuts off. 4 seconds later the rocket's altitude is 5100 meters.
What is the rockets acceleration during the 1st 16 seconds?

0=v+-9.8 m/s^2 *4s = 39.2m/s but I'm off by a factor of 10 for the velocity at 5100 m
 
Last edited:
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What have you done so far?
 
jenduncan said:
0=v+-9.8 m/s^2 *4s = 39.2m/s but I'm off by a factor of 10 for the velocity at 5100 m

What exactly are you going for here? The assigment does not say that the rocket is at halt at 5100m.
 
Call the acceleration asked for "a". Then, for the first 16 seconds, v(t)= at and
h(t)= (a/2)t2 (v(t) is the velocity t seconds after lift off, h(t) is the height t seconds after lift off). From that you can find the velocity, v(16), and height h(16) when the rocket shuts off as a function of a.

Now the acceleration is just -g: v(t)= v16- gt and h(t)= h16+ v16- (g/2)t2, where v16 and h16 are the speed and height of the rocket when the rocket shut off. t is, of course, the time after the rocket shut off so set h(4)= 5100 and you will have an equation in a. Solve that equation.

Notice that the mass of the rocket is irrelelvant.
 
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