Question

An astronaut must journey to a distant planet, which is 211 light-years from Earth. What speed will be necessary if the astronaut wishes to age only 15 years during the trip? (Give your answer accurater to five decimal places.) Hint: The astronaut will be traveling at very close to the speed of light. Therefore, approximate the dilated trip time At to be 211 years

Answer 1

At 99.7% of the speed of light

Step-by-step explanation:

For the astronaut traveling, the perceived time elapsed
`t'` with respect to the perceived time elapsed
`t` of an observer at rest with respect to the astronaut is:

`t'=t\sqrt{1-(v^2)/(c^2)}`

where c is the speed of light and v is the speed of the traveler.

Solving for v we have:

`v=c√(1-(t'/t)^2))\implies (v)/(c)=√(1-(t'/t)^2)}=99.7\%\,c`