Rivers carry sediment suspended in the water, and bouncing along on the river bed.    Starting off with a mixture of large rocks and mixed minerals in the Blue Ridge mountains, what winds up at the beach?  How does  the sediment of a mountain stream become the sediment of a beach ? (hint) The currents sort the material by size and weight, and the weathering of the minerals and rocks cause the load to change downstream.

As streams make their way down mountain slopes and across plains, energy not used to overcome obstacles and transport sediment can be used to make beautiful curves in the river path, known as meanders, in this way.
How fast is the erosion?  The Appalachians are generally thought to erode at 4 cm per thousand years (40 meters in a million years, that's REALLY slow).  The Himalayan erosion rate might be as high as several cm per year !  That's more than a kilometer per million years.  Remember that a million years is a drop in the bucket in geologic time.

I say if you erode a mountain, it won't disappear. You say, huh?
Think about this.  If you're standing on an iceberg and you mark the "shore" with a pen, and then you chip off all the ice above the line...what happens? Will you still be standing at the water level or not?

 Think about it then look at this page.  Mountains are really just thick sections of crust that "float" above the mantle and must be thinned before they disappear
 

Find information about your own watershed here.
More information on rivers here.