18. distances in space are often quoted in units of light years, the distance light travels in one year. (a) how many meters is a light year? (b) how many meters is it to andromeda, the nearest large galaxy, given that it is 2.00×106 light years away? (c) the most distant galaxy yet discovered is 12.0×109 light years away. how far is this in meters?

a) d = 9,454 10¹⁵ m, b)  18.9 10²¹ m  c) 113 10²⁴ m

Explanation:

The light years unit is used because the distances are so large that it is not very manageable.

The speed the light is the space is

    c = 2,998 10⁸ m /s

a) As the speed is constant we can use the equations of uniform motion

    t = 1 year (365 days / 1 year) (24 h / 1 day) (3600 s / 1h) = 3.1536 10⁷ s

    c = d / t

    d = c / t

    d = 2,998 10⁸ 3,136 10⁷

    d = 9,454 10¹⁵ m

b) let's transform is distance to meters

    d = 2.00 10⁶ light year (9,454 10¹⁵ m / 1 ly)

    d = 18.9 10²¹ m

c)

     d2 = 12.0 10⁹ ly (9,454 10¹⁵ /1 ly)

     d2 = 113 10²⁴ m

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min