# Vector Valued Function Spaceship Problem

1. Jan 27, 2013

### Baumer8993

1. The problem statement, all variables and given/known data
We are doing vectored valued functions currently in calculus. The Problem is:

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 ship. When should the engines be turned off?

2. Relevant equations

The position function of the spaceship is

R(T) = <3+T, 2+ln(T), 7-(4/(T2 +1)>

3. The attempt at a solution

I think I need to take the derivative to get the velocity function. The only problem is it is hard to find the correct location in which the velocity vector would be parallel, and on point to the space station.

2. Jan 27, 2013

### tiny-tim

Hi Baumer8993!
That's right …

and then the vector from the spaceship to the target is R(T) - (6,4,9)

3. Jan 27, 2013

### Baumer8993

OHHHHHHHHHH!!!! Thank you so much!

4. Jan 27, 2013

### LCKurtz

Of course, with the engine off, he will crash into the dock, but never mind that

5. Jan 27, 2013

### tiny-tim

it's one of those new space stations that can slow spaceships down!

(a combination of magnetic fields and graphene-based elastic)