When swimming across a river you swim to the east at 1.0 mph while the river flows southward at 2.4 mph. Your velocity is a superposition of these two velocities. What is your speed (i.e. the magnitude of your velocity)?

i have no idea how to do this please help

To find the speed (magnitude of velocity) when swimming across the river, you can use vector addition. Here's how to do it:

1. Label the two velocities:
- The velocity at which you swim to the east is 1.0 mph to the right (positive x-axis direction).
- The velocity of the river flowing southward is 2.4 mph downward (negative y-axis direction).

2. Convert both velocities into vector form:
- The velocity of swimming to the east is (1.0 mph, 0 mph).
- The velocity of the river flowing southward is (0 mph, -2.4 mph).

3. Add the two vectors together to get the resultant velocity:
To add the vectors, you simply add the corresponding components:
(1.0 mph, 0 mph) + (0 mph, -2.4 mph) = (1.0 mph, -2.4 mph)

4. Find the magnitude of the resultant velocity:
The magnitude of a vector is calculated using the Pythagorean theorem:
magnitude = sqrt((x^2) + (y^2)).
In this case, the magnitude = sqrt((1.0 mph)^2 + (-2.4 mph)^2)
magnitude = sqrt(1.0^2 + 2.4^2) mph
magnitude = sqrt(1 + 5.76) mph
magnitude = sqrt(6.76) mph
magnitude ≈ 2.60 mph (rounded to two decimal places)

Therefore, the speed (magnitude of your velocity) when swimming across the river is approximately 2.60 mph.