We present results from a 49.3 ks Chandra X-ray observation of the strongly interacting dumbbell galaxies NGC 4782 ( 3C278 ) and NGC 4783 that constrain the kinematics of the interaction and models for bending the radio jets associated with NGC 4782 . The galaxies are embedded in an approximately spherical distribution of group gas , centered on NGC 4782 , that , away from the interaction region , is nearly isothermal with mean temperature kT \sim 1.4 \pm 0.4 keV . The X-ray morphology suggests that NGC 4783 is infalling into a single , massive galaxy group ( LGG 316 ) with NGC 4782 nearly at rest at the center of the group potential . NGC 4783 shows a sharp X-ray surface brightness edge ( cold front ) to the east and a \sim 15 kpc ram-pressure-stripped tail to the west . Analysis of this cold front indicates NGC 4783 is moving east with a total velocity 870 ^ { +270 } _ { -400 } km s ^ { -1 } ( Mach 1.4 ^ { +0.5 } _ { -0.7 } ) at an inclination angle 46 ^ { \circ } ( > 33 ^ { \circ } ) towards us with respect to the plane of the sky . A \sim 45 Myr old X-ray cavity , with enthalpy of 4.4 \times 10 ^ { 57 } ergs , coincides with the eastern radio lobe of 3C278 . X-ray knots are found on both the radio jet and counter-jet , coincident with peaks in the radio emission . If we assume a light , mildly relativistic jet in 3C278 , then ram pressure velocities of 100 - 200 km s ^ { -1 } impacting the eastern jet and \sim 170 km s ^ { -1 } acting on the western radio lobe are sufficient to produce their observed bending . These velocities may be caused by bulk motions of the surrounding gas induced by the high velocity interaction between the galaxies , by the motion of the host galaxy NGC 4782 relative to the IGM , or a combination of these processes .