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

diagram is missing, but i will try to explain your doubt.

answer:

amplitude is the maximum displacement or distance moved on a point of a vibrating body or wave measured from its equilibrium position.it is equal to half the length of vibration path.