Question

Light takes 4 hours to cover the distance from sun to neptune if you travel in spaceship at speed 0.99c then approximately how much (in minutes) to required to cover the same distance measured with a clock on the spaceship?

Answer 1

Answer:

t = 4xroot (1- 0.99^2)

= 4xroot(1- 0.98)

=4xroot (0.02)

= 4x 0.141

= 0.56 h

1h=60min

0.56h= 0.56×60 min= 33.6 min

Answer 2

Answer:

It will show 33.86 minutes.

Explanation:

Here, what we take into concern is Time dilation.

It is a consequence of Einstein's general theory of relativity.

According to this, one experiences lesser time if he/she moves at a relative speed with something.

Now, as per your question, the formula for velocity time dilation goes like-

$\frac{T'}{T}=\sqrt{1-\frac{v^2}{c^2}}$

where,

T' is the time in frame of moving body,

T is time in frame of relative rest,

v is velocity of the moving body, and

c is the speed of light.

Now, if we solve this for v = 0.99c, we get

T' = 0.1411 T

that is,

T' ≈ 33.86 minutes ≈ 33 minutes 51 seconds.