Resident Paul Weir, whose Citroen was hit, is urging anyone with information to come forward.
He said: “If anyone knows the drivers of the silver BMW and black Mondeo that were racing on Warmsworth Road at 6.45pm, let me know who they are.
"They almost knocked a mother and child over, before running into the back of us at 70mph+ as we had just passed the One Stop and opposite Fairway.
"Then carried on and didn't stop. Scumbags. We spent three hours in A&E thanks to them, and are are lucky to be alive.
Paul made a call for futher trafflic calming safety measures or camera monitoring methods to be put in place on Balby Road and surrounding areas.
We have contacted South Yorkshire Police for information, anyone who knows anything should contact them on 101.