Question

A swimmer heading directly across a river 200 m wide reaches the opposite bank in 400 s during which time he is swept downstream 480 m.

how fast can he swim in still water?

Answer 1

The swimmer's velocity in still water is calculated using the velocity components across the river and downstream. The component across the river is 0.5 m/s, and the downstream component is 1.2 m/s. Combining these, the swimmer's velocity in still water is found to be 1.3 m/s.

Step-by-step explanation:

To determine how fast the swimmer can swim in still water, we need to consider the components of the swimmer's velocity and the current's velocity separately. Given that the swimmer is swept downstream 480 m while crossing a river that is 200 m wide, we can use to find the velocities.

First, we calculate the swimmer's velocity across the river (the y-component). The swimmer covers the 200 m width of the river in 400 s, so:

1. Velocity across the river (Vy) = distance / time = 200 m / 400 s = 0.5 m/s

Next, we calculate the swimmer's velocity along the river (the x-component). The swimmer is swept downstream 480 m in the same 400 s, so:

1. Velocity downstream (Vx) = distance / time = 480 m / 400 s = 1.2 m/s

The swimmer's velocity in still water is the magnitude of the resultant vector formed by these two perpendicular components:

1. Swimmer's velocity in still water (Vswimmer) = √(Vx2 + Vy2)
2. Vswimmer = √(0.52 + 1.22) m/s
3. Vswimmer = √(0.25 + 1.44) m/s = √(1.69) m/s
4. Vswimmer = 1.3 m/s

Therefore, the swimmer's velocity in still water is 1.3 m/s.