#### Answer

a) Samantha’s upstream displacement will be less than her downstream
displacement.
b) The displacement of Samantha and the lifejacket are the same.
c) Samantha’s total displacement relative to the water is zero
d) It takes the same time each way.

#### Work Step by Step

a)
In the reference frame of the river bank, Samantha’s upstream displacement will be less than her downstream displacement due to the motion of the water relative to the bank.
b)
When Samantha catches up to the lifejacket, they have both traveled the same distance downstream from the starting point of the kayaking trip; thus, the displacement of Samantha and the lifejacket in the reference frame of the river bank are the same.
c)
Since the lifejacket is at rest relative to the water, Samantha’s total displacement relative to the water is zero when she catches up with the lifejacket. Therefore, relative to the water, Samantha’s upstream and downstream displacements will be equal in magnitude and opposite in direction.
d)
In the reference frame of the water, she paddles equal distances at the same speed, so it takes the same time each way.