A space ship travels to Alpah Centauri which is about 4 light years away from earth. How far does this distance appear to you if you are on a space ship traveling at .99c?

Question

anonymous · Answer

@shamim

shamim · Answer

i think it will b the same formula

shamim · Answer

$$L=L _{0}\sqrt{1-\frac{ v ^{2} }{ c ^{2} }}$$

anonymous · Answer

what do L and L0 = ?

anonymous · Answer

@shamim

shamim · Answer

$$L _{o}=4 ly$$

shamim · Answer

we hv to calculate  L

anonymous · Answer

then what would v=?

anonymous · Answer

@Compassionate

compassionate · Answer

v = the velocity relative 
c= speed of light

compassionate · Answer

c = the speed of light
L0 = proper length
L = length at speed v
v = speed of the rocket

compassionate · Answer

You want to plug this in and solve for L.

anonymous · Answer

Use the formula for time dilation,
$$t=\frac{ t _{0} }{ \sqrt{1-\frac{ v ^{2} }{ c ^{2} }} }$$
whre, t= proper time 
t0= observed time.

anonymous · Answer

$$t=\frac{ 4*365*24*60*60 }{ \sqrt{1-\frac{ 0.99 ^{2}c ^{2} }{ c ^{2} }} }$$
I calculated the answer and its around$$8.99139\times10^{-7}$$
but you should confirm it by calculating it again.

anonymous · Answer

the answer is in years
8.99139*10^-7 years

anonymous · Answer

or the answer is 894211107.2 seconds

anonymous · Answer

@shamim,
The formula you have given(L=)
that is for length contraction, not time dilation.

anonymous · Answer

Thank you :) can you help me with another problem please?