Answer: 17.83 AU
Explanation:
According to Kepler’s Third Law of Planetary motion <em>“The square of the orbital period of a planet is proportional to the cube of the semi-major axis (size) of its orbit”. </em>
(1)
Talking in general, this law states a relation between the <u>orbital period</u> 
of a body (moon, planet, satellite, comet) orbiting a greater body in space with the <u>size</u> 
of its orbit.
However, if is measured in <u>years</u>, and is measured in <u>astronomical units</u> (equivalent to the distance between the Sun and the Earth: 
), equation (1) becomes:
(2)
This means that now both sides of the equation are equal.
Knowing 
and isolating from (2):
![a=\sqrt[3]{T^{2}}=T^{2/3}](https://tex.z-dn.net/?f=a%3D%5Csqrt%5B3%5D%7BT%5E%7B2%7D%7D%3DT%5E%7B2%2F3%7D)
(3)
(4)
Finally:
(5)
The age of the galaxy when we look back is 13.97 billion years.
The given parameters:
- <em>distance of the galaxy, x = 2,000 Mpc</em>
According Hubble's law the age of the universe is calculated as follows;
v = H₀x
where;
H₀ = 70 km/s/Mpc
Thus, the age of the galaxy when we look back is 13.97 billion years.
Learn more about Hubble's law here: brainly.com/question/19819028
We have to calculate the impulse of a hockey puck.
Imp = m * ( v 1 - v 2 ) = m * Δ v
v 1 = - 10 i m/s,
v 2 = ( 20 * cos 40° ) i + ( 20 * sin 40° ) j =
= ( 20 * 0.766 ) i + ( 20 * 0.64278 ) j = ( 15.32 i + 12.855 j ) m/s
Δ v = ( 15.32 i + 12.855 j ) - ( - 10 i ) =
= 15.32 i + 12.855 j + 10 i = 25.32 i + 12.855 j
| Δv | = √ ( 25.32² + 12.855²) = √806.35 = 28.4 m/s
Imp = 0.2 kg * 28.4 m/s = 5.68 N-s
Answer: D ) 5.68 N-s.
Time period = time/no. of waves = 6/3 = 2s
