A river is moving at 4.0 m/s [s] , and a swimmer swims across it at 1.4 m/s [e] relative to the water. What is the swimmers velocity measure with respect to the river bank

what is sqrt (4^2+1.4^2) ?

To find the swimmer's velocity with respect to the river bank, we need to use vector addition.

First, let's assign directions to the velocities. The river's velocity is given as 4.0 m/s [s], indicating a southward direction. The swimmer's velocity is given as 1.4 m/s [e], indicating an eastward direction.

To add these vectors, we can use the Pythagorean theorem to find the magnitude of the resultant velocity, and trigonometry to find its direction.

1. Start by squaring each velocity component:
River velocity: (4.0)^2 = 16.0
Swimmer's velocity: (1.4)^2 = 1.96

2. Add the squared components:
16.0 + 1.96 = 17.96

3. Take the square root of the sum to find the magnitude of the resultant velocity:
√17.96 ≈ 4.24 m/s

4. To find the direction, we can use the tangent function:
tanθ = y/x, where θ is the angle and x and y are the velocity components
tanθ = 4.0/1.4 ≈ 2.857

5. To find the angle θ, take the inverse tangent (arctan) of the result:
θ ≈ arctan(2.857) ≈ 68.96 degrees

Thus, the swimmer's velocity with respect to the river bank is approximately 4.24 m/s at an angle of 68.96 degrees east of south.