When should the engines be turned off?

  • Thread starter Thread starter meesa
  • Start date Start date
  • Tags Tags
    Spaceship
Click For Summary

Homework Help Overview

The problem involves determining the appropriate time for a spaceship to turn off its engines in order to coast into a space station. The spaceship's position is given as a function of time, and the coordinates of the space station are provided. The discussion revolves around the relationship between position, velocity, and acceleration in the context of motion in space.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the need to relate the spaceship's position and its derivatives to determine the timing for engine cutoff. Questions are raised about the derivatives of the position function and their implications for velocity and acceleration. Some participants express confusion about the completeness of available solutions and seek guidance on how to approach the problem without receiving direct answers.

Discussion Status

There is an ongoing exploration of the problem, with some participants providing insights into the nature of velocity and acceleration when the engines are turned off. Guidance has been offered regarding the differentiation of the position function and the implications for motion after engine cutoff. Multiple interpretations of the problem are being discussed, and there is no explicit consensus on a single approach or solution.

Contextual Notes

Participants note the constraints of the forum rules against providing complete solutions, which influences the nature of the discussion. There is also mention of potential errors in the derivatives being discussed, indicating a need for careful consideration of the mathematical details involved.

meesa
Messages
9
Reaction score
0

Homework Statement



The position of a spaceship is [itex](3 + t, 2 + ln(t), 7 - \frac{4}{t^2 + 1})[/itex] and the coordinates of the space station are (6, 4, 9). The captain wants the spaceship to coast into the space station. When should the engines be turned off?

Homework Equations



[itex]r' = (1, \frac{1}{t}, \frac{8t}{(t^2 + 1)^2})[/itex]

The Attempt at a Solution



Every solution I've found online, but none of them are complete, and I have no idea what I'm missing. So would somebody please just work out the entire problem? PLEASE? All the help online is very vague and the most I've gotten from it is that I need the derivative, but I can't figure out how to relate that and the original together to get something.

Thanks.
 
Last edited:
Physics news on Phys.org
meesa said:

Homework Statement



The position of a spaceship is [itex](3 + t, 2 + ln(t), 7 - \frac{4}{t^2 + 1})[/itex] and the coordinates of the space station are (6, 4, 9). The captain wants the spaceship to coast into the space station. When should the engines be turned off?

What is the acceleration when the engine is turned off? What happens to the velocity?

Homework Equations



[itex]r' = (1, \frac{1}{t^2}, \frac{8t}{(t^2 + 1)^2})[/itex]

Check your y-coordinate derivative. It's wrong.

The Attempt at a Solution



Every solution I've found online, but none of them are complete, and I have no idea what I'm missing. So would somebody please just work out the entire problem? PLEASE? All the help online is very vague and the most I've gotten from it is that I need the derivative, but I can't figure out how to relate that and the original together to get something.

Thanks.

Sorry, no one is allowed to give full solutions to HW problems here. It's in the rules.

We can help you think through things though.
 
Last edited:
The acceleration would be zero. We're in mystical space where everything is perfect with lovely numbers.

Fixed the y derivative.

I've seen full solutions here before.

The answer is 1 according to the back of the book.
 
meesa said:
Fixed the y derivative.

I've seen full solutions here before.

Those were in contravention of the rules if they were solutions to homework problems. You can PM a mentor or admin if you have an issue with the policy.

The answer is 1 according to the back of the book.

I can guide you through the general approach if you answer the questions I asked in my previous post (acceleration, velocity).
 
Just saw that and edited my post right before yours came though. r' is the velocity.

A general approach will work, if you can do it without being too abstract. Appreciate your time.
 
meesa said:
Just saw that and edited my post right before yours came though. r' is the velocity.

A general approach will work, if you can do it without being too abstract. Appreciate your time.

Please start by answering my questions.

What happens to the acceleration when the engines are cut?

What happens to the velocity?
 
The acceleration would be zero. We're in mystical space where everything is perfect with lovely numbers.

The velocity would be constant, since acceleration is zero. What I wrote in my first post is the exact question.
 
meesa said:
The velocity would be constant, since acceleration is zero. What I wrote in my first post is the exact question.

I'm sorry I didn't notice you had answered earlier.

OK, what you have is a vector equation for displacement.

s(t) = sx(t) i + sy(t) j + sz(t) k

where i, j and k are the usual orthogonal unit vectors for 3-D. The individual expressions for the displacements along each axis are given in the original question.

Differentiate s(t) wrt t to find v(t) in the same form. You've already done the work here, just put it in vector form.

Now let the time when the engines are cut be T.

The displacement at at that time will be s(T).

The velocity at time T will be v(T).

Thereafter, the spaceship will move at the constant velocity v(T).

The displacement at any time t' (t'>T) will be given by:

(t' - T)v(T) + s(T) = s(t')

You want to equate s(t') to 6i + 4j + 9k and solve for T. You will have 3 equations in two variables, and if they can be solved to give consistent solutions, you have an answer.

EDIT: Confirmed that T = 1 is a consistent and valid solution. Now try it yourself.
 
  • Like
Likes   Reactions: 1 person

Similar threads

Vector Valued Function Spaceship Problem
  • · Replies 2 ·
Replies
2
Views
5K
How should I use the averaging approximation to find this?
  • · Replies 3 ·
Replies
3
Views
2K
How should I find the following period ## T ## of this solution?
  • · Replies 5 ·
Replies
5
Views
3K
How should I show that all solutions of this equation are bounded?
  • · Replies 4 ·
Replies
4
Views
2K
How should I find ## x_{2}(t) ## for this nonlinear integro-differential equation?
  • · Replies 6 ·
Replies
6
Views
3K
Calc III : Spaceship reaching a space station at constant velocity.
  • · Replies 4 ·
Replies
4
Views
3K
Velocity of the ball when it hits the ground, limits?
  • · Replies 17 ·
Replies
17
Views
3K
Find When Engines Should Be Turned Off for Spaceship to Reach Space Station
  • · Replies 6 ·
Replies
6
Views
3K
Domain of definition differential equations
  • · Replies 2 ·
Replies
2
Views
2K
When Should the Spaceship's Engines Be Turned Off?
  • · Replies 2 ·
Replies
2
Views
8K