If the boat heads eastward, directly across the river what are the direction and magnitude of its total velocity?A boat travels 4.0 m/s in still...

The total velocity is the vector sum of the velocity of
the boat and velocity of the river.

The vector of velocity
of the boat is perpendicular to the velocity vector of the
river.

We can draw the diagram of velocity vectors where
the hypothenuse of the right angle triangle is the resulting
velocity.

The hypothenuse is calculated using Pythagorean
theorem:

v^2 = (boat's velocity)^2 + (river's
velocity)^2

v^2 = (4 m/s)^2 + (5.5
m/s)^2

v^2 = 117625
(miles/hour)^2

v total= 6.8
m/s

The magnitude of the total velocity of
the boat is the angle that the direction of the boat makes with the east
direction.

tan a = river's velocity/boat's
velocity

tan a = 5.5/4

tan a =
1.375

a = 54
degrees

The total velocity of
the boat is v = 6.8 m/s at 54 degrees south of
east.