Although not that common there is nothing special about a rainbow "hitting the ground" as the image below shows.
You can think of the ground as getting in the way of the rainbow being a complete circle as shown in this next image taken from an airplane
during a thunderstorm with the ground not causing an obstruction.
Without getting too far into the details of the formation of a rainbow the diagram below illustrates the location, in terms of angle not distance, of a rainbow.
Notice the line from the Sun passing through the observer to the anti-solar point which is the centre of the rainbow.
During the morning the line rotates towards the vertical so the anti-solar point goes further down below the ground level and less of the rainbow is seen.
If the Sun is high enough in the sky then no rainbow is seen.
On the other hand when the observer is in an airplane the anti-solar point can be well above ground level and so a complete rainbow can be seen.
There are many videos of "the end of the rainbow" seen whilst travelling in a car.
This video illustrates that “the end of a rainbow” depends on the position of the observer (in the car) because as the observer moves so does “the end of the rainbow”.
Atmospheric optics is a website which is worth a visit as it illustrates the formation of various types of rainbows including those formed by reflection.