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

option c) 0.88c is the correct answer

Step-by-step explanation:

using the Lorrentz equation we have

`t=(d)/(v)\sqrt{1-((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=(15years* c)/(v)\sqrt{1-((v)/(c))^2}`

or

`((v)/(c))^2* ((8)/(15))^2=1-((v)/(c))^2`

or

`((v)/(c))^2* 0.284=1-((v)/(c))^2`

or

`((v)/(c))^2* 0.284 + ((v)/(c))^2 =1`

or

`(1.284* (v)/(c))^2 =1`

or

`((v)/(c)) =\sqrt{(1)/(0.284)}`

or

`v=0.88c`