Answering Relativity Questions: Earth, Spacecraft, Lorentz Transforms

[uranium_235]

A friend gave me these questions to answer.

"A certain star is 7.0 light years away. How long would it take a spacecraft traveling at .950c to reach that star from Earth, as measured by observers (a ) on Earth (b )on the aircraft (c ) what is the distance travled according tio observers on the spacecraft ? (d ) what will the spacecraft occupants compute their speed to be from the results of (b ) and (c )?"

I fear taking the obviouse path, for it may take me to answer which contradicts that which you would get if you applied the lorentz transformations, which I know nothing of. What would be the correct way of going about this question?

and this was the second question.

"Derive the general relativist equation of T = To sr (1 - v^2/c^2)"

I have no idea of how to go solving about this one.

 

[Nenad]

(a ) on earth.

$$v = \frac{d}{t}$$

$$t = \frac{d}{v}$$

$$t = \frac{7.0cy}{0.950c}$$

$$t = 7.4y$$

(b )on the aircraft.

$$t = t_o \sqrt{1-v^2 / c^2}$$

$$t = (7.4y) \sqrt{1-(0.950c)^2 / c^2}$$

$$t = (7.4y) \sqrt{1-(0.9025c^2 / c^2}$$

$$t = (7.4y) \sqrt{1-(0.9025)}$$

$$t = (7.4y) \sqrt{0.0975}$$

$$t = (7.4y)(0.3122)$$

$$t = 2.3y$$

(c ) what is the distance travled according tio observers on the spacecraft ?

$$d = d_o \sqrt{1-v^2 / c^2}$$

$$d = (7.0ly) \sqrt{1-(0.950c)^2 / c^2}$$

$$d = (7.0ly) \sqrt{1-(0.9025c^2 / c^2}$$

$$d = (7.0ly) \sqrt{1-(0.9025)}$$

$$d = (7.0ly) \sqrt{0.0975}$$

$$d = (7.0ly)(0.3122)$$

$$t = 2.19ly$$

(d ) what will the spacecraft occupants compute their speed to be from the results of (b ) and (c )?"

$$v = \frac{d}{t}$$

$$v = \frac{2.19ly}{2.3y }$$

$$v = 0.950c$$


Do you get it?

 

[uranium_235]

Do you get it?

Yes. I do get it.