#### Answer

a. 37.5m.
b. 75 seconds

#### Work Step by Step

Let the flow of the river be in the x direction and across the river be the y direction.
Let S denote Swimmer, R the River, and B the Bank. The pair “SB”, for example, represents the swimmer’s motion relative to the bank.
$$ \vec{v_{SB}} = \vec{v_{SR}} + \vec{v_{RB}} $$
$$= (0, 0.60 m/s) + (0.50 m/s, 0) $$
$$= (0.50 m/s, 0.60 m/s)$$
$$ \vec{v_{SB}} = (0.50 m/s, 0.60 m/s)$$
a. Find the downstream distance from analyzing the x-direction.
(0.50 m/s)(75 s) = 37.5 m.
b. Find the time to cross from analyzing the y-direction:
t = (45 m)/(0.60 m/s) = 75 seconds.