To solve this problem, we need to use vector addition to find the resultant velocity of Julia.
Let's assume that the east direction is the positive x-axis and the south direction is the negative y-axis.
The velocity of Julia in still water is 8 km/hr in the positive x-axis direction.
The velocity of the river is 3 km/hr in the negative y-axis direction.
To find the magnitude and direction of Julia's velocity, we need to find the resultant velocity vector, which is the vector sum of her velocity in still water and the velocity of the river.
Using the Pythagorean theorem, the magnitude of the resultant velocity can be calculated as:
|V| = √(Vx² + Vy²)
where Vx is the x-component of the resultant velocity and is equal to Julia's velocity in still water, and Vy is the y-component of the resultant velocity and is equal to the velocity of the river.
Vx = 8 km/hr
Vy = -3 km/hr
|V| = √(8² + (-3)²) = √(64 + 9) = √73 km/hr
The direction of the resultant velocity can be calculated as:
θ = tan⁻¹(Vy / Vx)
θ = tan⁻¹(-3 / 8) = -20.56°
The negative sign indicates that the resultant velocity vector makes an angle of 20.56° below the positive x-axis (east direction).
Therefore, the magnitude of Julia's velocity is approximately 8.54 km/hr, and the direction of her velocity is 20.56° below the positive x-axis (east direction).