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 water. The river flows southward at 5.5 m/s.
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.