Answer:
doppler shift's formula for source and receiver moving away from each other:
λ'=λ°√(1+β/1-β)
Explanation:
acceleration of spaceship=α=29.4m/s²
wavelength of sodium lamp=λ°=589nm
as the spaceship is moving away from earth so wavelength of earth should increase w.r.t increasing speed until it vanishes at λ'=700nm
using doppler shift's formula:
λ'=λ°√(1+β/1-β)
putting the values:
700nm=589nm√(1+β/1-β)
after simplifying:
β=0.17
by this we can say that speed at that time is: v=0.17c
to calculate velocity at an acceleration of a=29.4m/s²
we suppose that spaceship started from rest so,
v=v₀+at
where v₀=0
so v=at
as we want to calculate t so:-
t=v/a v=0.17c ,c=3x10⁸ ,a=29.4m/s²
putting values:
=0.17(3x10⁸m/s)/29.4m/s²
t=1.73x10⁶
