Special Relativity rocket’s speed

[br0shizzle1]

Homework Statement

A rocket flies between two planets that are one light-year apart. What
should the rocket’s speed be so that the time elapsed on the captain’s watch
is one year?

Homework Equations

I have v = d'/t'
d'=d/ϒ
t'=1 year
d=1 light year

The Attempt at a Solution

Will the equations I use vϒ=d/t' but I get complex roots as an answer. What am I doing wrong?

 

[TSny]

Hello and welcome to PF!

I believe you have it set up correctly. You'll need to show your algebra steps in order for us to see where you are making a mistake.

 

[br0shizzle1]

Hello and welcome to PF!

I believe you have it set up correctly. You'll need to show your algebra steps in order for us to see where you are making a mistake.

v(sqrt(1-(v/c)^2)=d/t
v^2(1-(v/c)^2)=d^2/t^2
v^2-v^4/c^2=d^2/t^2
v^2-v^4/c^2-d^2/t^2=0
I used wolfram to solve for roots and it gave back complex numbers.

 

[TSny]

v(sqrt(1-(v/c)^2)=d/t

Did you use the correct expression for ϒ?

 

[br0shizzle1]

Did you use the correct expression for ϒ?

oops, v^2/(1-(v/c)^2)=d^2/t^2
Should I multiply the LHS by the denominators conjugate?

 

[TSny]

oops, v^2/(1-(v/c)^2)=d^2/t^2

EDIT: OK

Should I multiply the LHS by the denominators conjugate?

No, try multiplying both sides by the denominator on the left side.

 

[br0shizzle1]

EDIT: OK



No, try multiplying both sides by the denominator on the left side.

Ah! thank you, everything works now.
edit: is there any way I can give your points or something of that regard?

 

[TSny]

Good work! Don't worry about any points.

 

[Harjot]

Ah! thank you, everything works now.
edit: is there any way I can give your points or something of that regard?

Hey! Would you mind sharing what you got as a result? I'm having a little trouble with the equation myself.

 

[BvU]

Hey! Would you mind sharing what you got as a result? I'm having a little trouble with the equation myself.

PF custom is to help find answers. So show your work to let us help you where you get stuck.

@br0shizzle1: TSny is too modest -- befitting someone of his (/her?) status in PF. But there is a "Like" link at the lower right in every posting (except your own :) ).

 

[Harjot]

PF custom is to help find answers. So show your work to let us help you where you get stuck.

@br0shizzle1: TSny is too modest -- befitting someone of his (/her?) status in PF. But there is a "Like" link at the lower right in every posting (except your own :) ).

Fair enough. I also had v(gamma)=d/t' --> (v^2)=((d^2)/(t'^2))*(1-(v/c)^2) --> here I considered d^2/t'^2 to be equal to c^2 because d=1 light year and t we set to 1 year so my equation became --> v^2 = c^2(1-(v^2/c^2)) --> (v^2)/(c^2) = 1-(v^2/c^2) --> ((v^2)/(c^2))+((v^2)/(c^2)) = 1 --> 2((v^2)/(c^2)) = 1 --> ((v^2)/(c^2)) = 1/2 ----> v/c=sqrt(1/2) and then v=sqrt(1/2)*c.

Appreciate the response :)

 

[BvU]

And where do you think you have trouble with the equation ?

Oh, and: Hello Harjo, welcome to PF! :)

A little unusual to make your debut tagging onto an existing thread, but your question is clear and it's a start...

 

[Harjot]

Oh I was just wondering if I had done it right. If my assumption was fair to make.

I realize now I should have put the work down first and then asked for clarification. woopsie daisy

 

[BvU]

You're doing fine. And, just so you know: I was surprised by the answer, too ! Shows you're never too old to learn

 

[Harjot]

Awesome! True enough :w

Thanks a bunch!