- #1

Baumer8993

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## Homework Statement

The position function of a spaceship is r(t)= < 3+T, 2+ln(T), 7 -(4/T

^{2}+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)/(T

^{2}+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/s

^{2}+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?