Question

A space probe is sent to the vicinity of the star Capella, which

is42.2 light years from the earth. (A light year is the
distancelight travels in a year.) The probe travels with a speed
of0.9910c. An astronaut recruit on board is 19 yearsold
when the probe leaves the earth. What is her biologicalage when the
probe reaches Capella?

Answer 1

24.70 yrs

Step-by-step explanation:

Using length contraction formula

where v = 0.9910c, Lo = 42.2 light years

L = L₀
`\sqrt{1 - (v^(2) )/(c^(2) ) }` = 42.2
`\sqrt{1 - (0.9910c^(2) )/(c^(2) ) }` = 5.649 yr

to=
`(L)/(v)` = 5.649 c.yr / 0.9910c = 5.70yrs

the biological age of Capella = 19 + 5.70 yr = 24.70 yrs