To solve this vector addition problem, we need to use the component method of vector addition. We can break down the vectors into their horizontal and vertical components and then add them separately.
The vector 15 km E can be broken down into a horizontal component of 15 km and a vertical component of 0 km. The vector 20 km S can be broken down into a horizontal component of 0 km and a vertical component of -20 km.
We can now add the horizontal components and vertical components separately to get the resultant vector. The horizontal component is 15 km and the vertical component is -20 km.
Using the Pythagorean theorem, we can find the magnitude of the resultant vector:
magnitude = sqrt(horizontal_component^2 + vertical_component^2)
= sqrt(15^2 + (-20)^2)
= sqrt(225 + 400)
= sqrt(625)
= 25 km
Therefore, the magnitude of the resultant vector is 25 km. To find the direction of the resultant vector, we can use trigonometry. The angle between the resultant vector and the horizontal axis is given by:
theta = arctan(vertical_component / horizontal_component)
= arctan(-20 / 15)
= -53.13 degrees
Therefore, the resultant vector is 25 km at an angle of 53.13 degrees below the horizontal axis.