Jim and his family listened to the evening news anxiously for any report of further advances by the military forces. When they heard the reporter announce that the army was pressing forward and would reach their area by nightfall, Jim decided that it was necessary that the family evacuate that very night, rather than waiting for morning as previously planned. However, the recently-retired Colonel Jim had secret documents in the house which could not be found by the attacking army. Colonel Jim urged his family to take the car and proceed to the train station. He would remain to burn the documents, then attempt to catch up with them later on.
Just as the Colonel finished burning the last of the documents, he glanced at his watch. It was too late. The train would have already departed. Nevertheless, he leaped on his motorbike, and gunned the engine. As he glanced at the horizon, he caught site of the train in the distance. The train was heading directly east of the station, heading for a bridge lying up ahead. He estimated that the train had already done 1 km and that it had 2 km more to go before reaching an upcoming bridge. After the train had passed over the bridge, Jim would not be able to catch up with it, for he could not pass over the bridge on his motorbike. Jim knew that his house was exactly 4 km directly south of the train station. The train itself was .5 km long, and travelled at 50 km an hour.
Would it be possible for Jim to make it to the train and jump aboard before it passed over the bridge? What speed would he have to be going?