Time dilation and interstellar travel

[Fewmet]

Homework Statement

Plans are made to send a spaceship from Earth to a nearby star 10 light-years away and at rest with respect to Earth. The light support systems within the spacecraft will last for a year. (a) what is the minimum speed of the spacecraft relative to the Earth-star system if the crew is to survive the trip? (b) If time we mot dilated, what minimum speed would be necessary for the trip?

Homework Equations

the time dilation equation

The Attempt at a Solution

a)From an observer on Earth, the velocity of the ship is the rest length (10 ly) divided by the relativistic time corresponding to the 10 years of life support.
v=L₀/$\gamma$T

v=10 ly/$\gamma$10y

Solving, I get v=0.707c

The back of the book (which has had two mistakes this chapter) says v=0.99c for part a.

Is my initial equation in error?

b) It looks to me like the answer is v=10 ly/y=c. The book's answer is 10c.

 

[Fewmet]

Never mind: it was a stupid mistake. I transcribed the problem correctly, but I got into my head that the rest time was 10 years, not the given 1 year.

It is good to know my method worked. It was kind of cool to need to substitute a rest length and a relativistic time into a classical equation.