A swimmer can swim at 3.9m/s in still water. What will the swimmer's speed be (relative to the shore) if he crosses a river that is flowing at 5.1m/s?
To find the swimmer's speed relative to the shore, we need to consider the vector addition of the swimmer's velocity and the velocity of the river.
The key idea here is to break down the velocities into their horizontal and vertical components. Let's assume the swimmer is moving directly across the river. In this case, the horizontal component of the swimmer's velocity is equal to their speed in still water (3.9 m/s), and the vertical component remains zero.
The river's velocity can also be broken down into horizontal and vertical components. Since the river is flowing perpendicular to the swimmer's path, its vertical component is zero. The horizontal component of the river's velocity is equal to its speed, which is given as 5.1 m/s.
Now, to find the swimmer's velocity relative to the shore, we add the respective horizontal components of the swimmer's and river's velocities.
Horizontal component of the swimmer's velocity = 3.9 m/s
Horizontal component of the river's velocity = 5.1 m/s
Adding these values together, we get:
3.9 m/s + 5.1 m/s = 9.0 m/s
Therefore, the swimmer's speed relative to the shore will be 9.0 m/s.