Answer:
(a). 12.43 years.
(b). 3.89 × 10^ -9 kg.
Explanation:
So, we are given the following data or parameters or information which is going to assist us in solving this question;
=> " mission from Earth to the distant star Sirius has a light year = 8.7 light years away. "
=> "The spaceship can travel with 70% the speed of light"
=> " The spaceship's cylinder shape has a diameter of 6 meters at the front surface and a length of 25 meters. "
=> density = 1 hydrogen atom/m^3.
Step one: convert light year to metres.
J = 8.7 × 9.461 × 10^15 = 8.23 × 10^16 m.
Step two: convert percentage speed of light to metre per seconds;
70% = 70/100 = 0.7.
U = 0.7 × speed of light = 0.7 × 3.0 × 10^8 = 2.1 × 10^8 m/s.
(a).
Step three: determine the time taken(convert to years);
J / U = time taken; = 8.23 × 10^16 m/ 2.1 × 10^8 m/s = 12.43 years.
(b). The mass of interstellar gas that collides with your spaceship during the mission;
Volume= {(6m)^2 × 22/7}/ 4 × ( 8.23 × 10^16 m). = 2.33 × 10^18 m^3..
Density = mass/volume .
Mass= [24 × 365 × 3600 × 3 × 10^8 × 8.7 × 1.673 × 10^-27 × 6^2 × 22/7]/4 = 3.89 × 10^ -9 kg.
