Yes, Sam is liable to Nathan. As Sam involved in rescuing Nathan, he is responsible for the additional injury happened to Nathan.
Step-by-step explanation:
On seeing Nathan’s helpless state, Sam decided to take him to the hospital. It expresses his duty of care. Sam is not responsible for the injuries that happened before he rescued Nathan.
But out of humanity Sam came forward to help Nathan. He took him in his car and started to drive towards the hospital. But due to Sam’s negligence, he drove the car into the ditch. This caused additional injury to Nathan.
Now Sam is responsible for this event. Once he decided to rescue Nathan, he should have driven carefully to the hospital.