Hint: Mechanics of Materials
A garden hose has stopped flow. There is constant static pressure and no water hammer. Why does the hose tear in the axial direction at the end of the hose?
If you assume a thin wall pressure vessel, rho_long = pr/2t while rho_hoop = pr/t. Since hoop stress is twice as large as longitudinal stress, the hose will tear axially.
As @Dexter_Kenta_Yanagis mentions, this problem disguises a garden hose as a thin-walled pressure vessel, which is commonly covered in Mechanics of Materials courses.
In a cylindrical vessel with Pressure P, there are 2 stresses to consider: hoop stress trying to pull the cylinder apart radially, and longitudinal (axial) stress trying to pull the cylinder apart axially.
A visual representation of the hose as a thin-walled pressure vessel is shown here, where you can see the directions in which hoop and longitudinal stress act.
The equations for the two stresses are:
where P = pressure, R = radius of the cylinder, & T = thickness
Since the hoop stress is twice of the longitudinal stress, the hose will tear axially. Think of a hotdog cracking along the longitudinal direction first (i.e. skin fails from hoop stress generated by internal pressure!)