In a train moving due north at \(3.1 \mathrm{~m} / \mathrm{s}\) relative to Earth, a passenger carrying a suitcase walks due north down the aisle at \(1.2 \mathrm{~m} / \mathrm{s}\) relative to the train. A spider crawls along the bottom of the suitcase at \(0.5 \mathrm{~m} / \mathrm{s}\) due south relative to the suitcase. What is the velocity of the spider relative to Earth?