#### Answer

a. B=D, A=C
b. D, C, A=B

#### Work Step by Step

a. The magnitude of Jake's momentum relative to the flatcar equals his mass multiplied by the magnitude of his velocity (aka speed) relative to the flatcar. He is moving fastest relative to the flatcar in situations B and D (tie), followed by situations A and C (also a tie).
b. Jake's velocity relative to the ground equals the sum of his velocity relative to the train, and the train's velocity relative to the ground. His velocities in the 4 cases, ABCD, are 4 m/s, -4 m/s, 10 m/s, and 12 m/s.
The magnitude of his momentum equals his mass multiplied by the magnitude of his velocity (aka speed). He is moving fastest in situation D, then C, followed by a tie between A and B.