Vector Valued Function Spaceship Problem

In summary: Please refer to the previous thread for the solution. In summary, you are trying to find the time at which the spaceship's velocity vector points towards the space station, which can be done by setting the velocity vector equal to the vector from the spaceship's position to the space station. Solving for t will give you the time at which the engines should be turned off.
  • #1
Baumer8993
46
0

Homework Statement



The position function of a spaceship is r(t)= < 3+T, 2+ln(T), 7 -(4/T2+1)> , and the coordinates of a space station are (6, 4, 9). The captain wants to coast into the space station. When should the engines be turned off?

Homework Equations


I took the derivative of the position function to get the velocity function:
V(t)= <1, (1/T), (8T)/(T2+1)2


The Attempt at a Solution



Right now I have a vector I called U =<6-3+s>, 4 -(2+ln(s)), 9-[7-(4/s2+1)]
I got this hint from my professor. I understand that this is the position vector to the spaceship at time s. I know I now need to find the velocity vector that is parallel to the position vector. My professor gave me the hint to multiply by a constant K in the velocity vector function. At that point I would have two equations, and two unknowns which is easy to solve. I am just stuck on when I multiply by the constant K what would I set the velocity vector function equal too?
 
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  • #2
When the engines are switched off, the spaceship will probably move in a straight line. So you want to switch them off when your velocity vector points from r(t) towards the space station.
 
  • #3
This is a repost of

https://www.physicsforums.com/showthread.php?t=667299

Why are you reposting a question that has already been replied to?
 

1. What is a vector-valued function?

A vector-valued function is a mathematical function that maps a set of input values to a set of output values, where both the input and output are vectors. This means that the function takes in multiple values and produces multiple values as its output.

2. What is the "spaceship problem" in relation to vector-valued function spaces?

The "spaceship problem" is a hypothetical scenario often used to illustrate the concept of vector-valued function spaces. In this problem, a spaceship is moving through space, and its position and velocity at any given time can be represented as vectors. The goal is to use vector-valued functions to model and predict the spaceship's motion.

3. How are vector-valued function spaces used in science?

Vector-valued function spaces are used in a variety of fields in science, such as physics, engineering, and computer science. They are used to model and analyze complex systems and phenomena, such as motion, electricity, and fluid dynamics. They are also used in optimization and control problems.

4. What are some common applications of vector-valued function spaces?

Some common applications of vector-valued function spaces include predicting and controlling the motion of objects, modeling electromagnetic fields, simulating fluid flow, and analyzing the behavior of circuits and control systems. They are also used in computer graphics and animation to create realistic movements and effects.

5. What are some key concepts to understand when working with vector-valued function spaces?

Some key concepts to understand when working with vector-valued function spaces include vector operations, such as addition and multiplication, vector calculus, and vector algebra. It is also important to understand how to graph and interpret vector-valued functions and how to use them in practical applications.

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