Question

A certain strain of bacteria doubles in number each 20 days. Two of these bacteria are placed on

a spaceship and sent away from the Earth for 1000 Earth-days. During this time, the speed of the
ship is 0.9950c. How many bacteria are aboard when the ship lands on the Earth​

Answer 1

Step-by-step explanation:

We shall apply time dilution relation of relativity

t =
`\frac{t_0}{\sqrt{1-(v^2)/(c^2) } }`

`1000 = \frac{t_0}{\sqrt{1-(v^2)/(c^2) } }`

`1000 = \frac{t_0}{\sqrt{1-(0.995^2)/(1) } }`

t₀ = 1000 x .09987

= 99.87 days .

doubling time = 20 days

no of doubling time in 20 days ; n = 99.87 / 20

n = 4.9935

n =
`n_0* 2^n` ; n₀ is initial number , n is number finally .

= 2 x 2⁴°⁹⁹³⁵

= 64 approx .