Question

A planet is 15 light years from earth. At which of the following speeds will the crew of a spaceship complete the trip to the planet in 8 years?
A) 0.78c

B) 0.85c

C) 0.88c

D) 0.92c

Answer 1

Answer:

option c) 0.88c is the correct answer

Explanation:

using the Lorrentz equation we have

$t=\frac{d}{v}\sqrt{1-(\frac{v}{c})^2}$

where,

t = time taken to cover the distance

d = Distance

v = velocity

c = speed of light

given

d = 15 light years

Now,

$8years=\frac{15years\times c}{v}\sqrt{1-(\frac{v}{c})^2}$

or

$(\frac{v}{c})^2\times (\frac{8}{15})^2=1-(\frac{v}{c})^2$

or

$(\frac{v}{c})^2\times 0.284=1-(\frac{v}{c})^2$

or

$(\frac{v}{c})^2\times 0.284 + (\frac{v}{c})^2 =1$

or

$(1.284\times \frac{v}{c})^2 =1$

or

$(\frac{v}{c}) =\sqrt{\frac{1}{0.284}}$

or

$v=0.88c$