A 0.14-km wide river flows with a uniform speed of 4.0 m/s toward the east. It takes 20 s for a boat to cross the river to a point directly north of its departure point on the south bank. What is the speed of the boat relative to the water?
A) 5.7 m/s
B) 8.5 m/s
C) 8.1 m/s
D) 7.0 m/s
E) 6.4 m/s

Question

Quizplus · Accepted Answer

Let's call the speed of the boat relative to the water "v". We can break the boat's motion into two components: a horizontal component (in the direction of the river's flow), and a vertical component (perpendicular to the river's flow). The horizontal component of the boat's velocity is the same as the river's velocity, which is 4.0 m/s. 
To find the boat's vertical velocity, we can use the fact that it takes 20 s to cross the river. During this time, the boat will travel a distance of 0.14 km (the width of the river). Therefore, its vertical velocity is given by the equation:
0.14 km = (v vertical velocity) x (20 s)
Solving for v vertical velocity, we find:
v vertical velocity = 0.007 km/s = 7.0 m/s
Now that we have both the horizontal and vertical components of the boat's velocity, we can use the Pythagorean theorem to find the boat's speed relative to the water:
v = sqrt((4.0 m/s)^2 + (7.0 m/s)^2)
v = 8.1 m/s

A 014-Km Wide River Flows with a Uniform Speed of 4