Answer:3.49 m/s
Explanation:
Given
Speed of marble at Bottom 
Diameter of loop 
As Energy is conserved therefore Energy at top is equal to energy at bottom

,where
is the velocity at bottom







If you are asking for a proof on having at least 3 dimensions in space, you can find the physical proof anywhere in your daily life activities. Just the fact that solids have volumes is a proof already that we live in a three-dimensional space. We can move forwards, backwards, sidewards and in all other directions possible.
When you go right into detail, the fundamental laws governing these proofs are very technical. They have differential equations to show as proof. It is too detailed to discuss here. The important things is that, these fundamental laws are what explains the science in our basic activities and natural phenomena:
*Gravitation and planetary motion
* Translation, rotation, magnetic field, forces
* Integrals of equations:
Answer:

Explanation:
Assuming the pith balls as point charges, we can calculate the repulsive force between them, using Coulomb's law:

We observe that the magnitude of the electric force is directly proportional to the product of the magnitude of both signed charges(
) and inversely proportional to the square of the distance(d) that separates them.
Replacing the given values, where k is the Coulomb constant:

Answer:
2.11 m/s
Explanation:
Take north to be positive and south to be negative.
Average velocity = displacement / time
v = (82 m + -44 m) / (14 s + 4 s)
v = 2.11 m/s
The velocity is positive, so it is 2.11 m/s north. The magnitude of the velocity is 2.11 m/s.