A steamboat moves with velocity components of 6 km/hr along the x direction and 8 km/hr along the y direction. what is the direction of the steamboat with respect to the x axis?

Refer to the diagram shown below.

The resultant velocity of the steamboat, V, is the vector sum of Vx and Vy.

The magnitude of V is

V = √ (6² + 8²) = 10 km/h

The angle which V makes above the x axis is

θ = tan⁻¹ (Vy/Vx) = tan⁻¹ (8/6) = 53.13°

Answer:

The steamboat moves at 10 km/h, at an angle of 53° above the x axis.