Answer:
The total momentum of the system before the collision is 0.0325 kg-m/s due east direction.
Explanation:
Given that,
Mass of the cart, m = 250 g = 0.25 kg
Initial velocity of the cart, u = 0.31 m/s (due right)
Mass of another cart, m' = 500 g = 0.5 kg
Initial velocity of the another cart u' = -0.22 m/s (due left)
Let p is the total momentum of the system before the collision. It is given by :

So, the total momentum of the system before the collision is 0.0325 kg-m/s due east direction.
The magnitude of vector b is 8.58 Unit.
Since both the vectors a and b are perpendicular to each other, so we can apply the Pythagoras theorem to calculate the magnitude of the vector b.
Applying the Pythagoras theorem
(a-b)^2=a^2+b^2
15^2=12.3^2-b^2
b=8.58 unit
Therefor the magnitude of the vector b is 8.58 unit.
When you square the "year" of each planet and divide it by the cube of its distance, or axis from the sun, the number would be the same for all the planets