1. The problem statement, all variables and given/known data
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?
2. Relevant equations
[itex]r' = (1, \frac{1}{t^2}, \frac{8t}{(t^2 + 1)^2})[/itex]
3. 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.
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?
2. Relevant equations
[itex]r' = (1, \frac{1}{t^2}, \frac{8t}{(t^2 + 1)^2})[/itex]
3. 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.
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