Hot Pursuit?

At 11:30 p.m. Dr. and Mrs. David Alberstrom returned to their suburban Washington home from a night at the opera. As Dr. Alberstrom entered the living room, he was attacked by a knife-wielding man coming from the dining room. Dr. Alberstrom and the stranger struggled for some minutes, but the intruder escaped, leaving the doctor wounded on the floor. Mrs. Alberstrom rushed to help her husband. She noticed that he had been stabbed and was bleeding. They got into their car to go to the hospital, with the doctor behind the steering wheel. Proceeding down the country road leading from the Alberstrom house, the doctor noticed a man running along the side of the road. As the car drew even with the man, it swerved sharply to the right, striking the man and coming to rest in a ditch at the side of the road. Dr. Alberstrom was slumped over the wheel unconscious. An ambulance called to the scene took both Dr. Alberstrom and the injured pedestrian to the hospital. Dr. Alberstrom died of his knife wounds without regaining consciousness. The pedestrian recovered from his injuries and was subsequently charged with attempted robbery and the murder of Dr. Alberstrom.

At defendant's trial the prosecution offers Mrs. Alberstrom's testimony to the above on the issue of the identity of the knife-wielding intruder. Defendant objects. What ruling and why? What result if Mrs. Alberstrom's proffered testimony included Dr. Alberstrom's exclaiming "That's him!" just before the car swerved into the defendant?