Why does Coriolis point this way intuitively? 
The Coriolis force points as is shown. I understand it mathematically.
I want an intuitive picture how it's true
Say I'm in the rotating frame of the earth and I look at the particle in the northern hemisphere moving up. Due to my rotating I'll see it go opposite to my sense of rotation as its evident from  geometry but the forces as are shown in the figure suggest the contrary!
Can anyone please help
 A: No you would not. It will appear to  go in the direction shown in the diagram.
Let’s say the object is fired from the equator toward the North Pole. Because of conservation of momentum, the object will retain its tangential velocity it obtained from the earth’s rotation at the equator.
Now the object moves in a direction (towards the north) where the average radius of the earth is decreasing, but the object retains its (tangential) velocity it had at the equator, so that it will appear to drift ahead at higher latitudes (since it travels a greater distance over a smaller radii in similar successive amounts of time) due to the fact that the velocity at the equator is higher than the (ground)  velocities at these higher latitudes  (smaller radii).
As you can see from the diagram, the exact opposite is true in the case of an object fired from the South Pole to the north. In this case it has a smaller tangential velocity, and as it travels to regions of higher radii, it will appear to drift to the left.
A: In part this is a equation about relative velocities.
Consider an observer, $a$, at rest relative to the axis of rotation of the Earth looking down at the Earth.

At the equator the speed of the ground relative to the observer looking down at the Earth is $v_{\rm ea}$ in an easterly direction.
Before it is projected the object is at rest relative to the ground so the speed of the object relative to the observer looking down at the Earth in an easterly direction is $v_{\rm ea}$.
Imagine the object at the Equator projected in a northerly direction with a speed $v$ relative to the observer/ground.
That object will also have a speed $v_{\rm oa}=(v_{\rm ea})$ in an easterly direction relative to the observer due to the rotation of the Earth.
As the object moves in the general direction of the north pole it maintains constant speeds $v$ and $v_{\rm oa}$ because there are no external horizontal forces acting on the object.
At position $c$ the speed of the ground under the object relative to the observer in an easterly direction is $v_{\rm ga}$.
This means that the speed of the object in an easterly direction relative to the ground is $v_{\rm og} =v_{\rm oa} - v_{\rm ga}$ ie the object as well as travelling in a northerly direction relative t the ground is also travelling in an easterly direction relative to the ground.
So to an observer standing on the ground how does one explain the object starting off at the equator not moving eastwards and yet at position $c$ having a component of velocity, $v_{\rm og}$, in a easterly direction, ie relative to an observer on the ground the object is accelerating in an easterly direction?
Introduce a (fictitious) force, $F_{\rm H}$, acting in an easterly direction which will mean that to an observer on the ground can use Newton first two laws.
In the Southern hemisphere assume that the object is projected northwards with a speed $v$ but in this case the ground is not moving relative the observer looking down on the Earth.
When the object reaches position $d$ to the observer looking down on the earth it only has a velocity in the northerly direction.
However an observer on the ground who is moving with a speed $v_{\rm ga}$ in an easterly direction sees the object moving as speed $v_{\rm og}=v_{\rm ga}$ in a westerly direction.
So to an observer on the ground the object has accelerated in a westerly direction and to make Newton's first two laws of motion work for an observer on the ground introduce a (fictitious) force, $F_{\rm H}$, acting in a westerly direction.
A: The closer you are to the equator, the faster you're spinning. When you travel away from the equator, you're bringing some of that speed with you
