How does plate tectonics to explain the hard rock we find in manhattan? more than 4 sentences

As continents move, they collide and rift according to a model known as the Wilson Cycle. The Wilson Cycle can be summed up as follows:

A stable continent begins to rift apart in order to accommodate heat escaping from the mantle. 

As the rift forms, the continent is stretched and thinned, and faults lead to some mild deformation. 

Magma intrudes into the continent and erupts onto the surface.

The continent is split and the sides pushed away from each other. 

As the plate margins separate, they undergo a period of calm. Sediments are deposited and build up in layers. 

Eventually, the margin will begin to move towards another continental margin. The ocean crust will subduct under the continental crust (due to the densities of the materials in the different crust). 

Volcanoes will form and collide with the margin (Mt. St. Helens is a modern example of such a volcanic arc). 

Eventually, the continental margins are close enough that they collide with each other, forming a mountain range (the Himalayans are a modern example). 

Each stage of the Wilson Cycle will produce different types of rocks.  When rifting, basalts and other mafic igneous rocks form. During the stable, calm phase, sedimentary rocks are formed. Volcanic arcs during the closing form igneous rocks, and the continental collision forms metamorphic rocks. 

Manhattan is an example of a continental margin that has undergone this process. It is currently in its second stage of calm. The rocks that are now there were deposited during the calm phase of the last cycle, and then metamorphosed during the formation of the supercontinent Pangea into the rocks that are now present.