Question

Consider a boat heading due east at 15 miles/hour. The water's current is moving at 7.1 miles/hour at 45º south of east. Drag vectors for the boat and the current into the vector addition simulation.
What do Rx, Ry, , and |R| represent in terms of the force of the current, and what do they represent in terms of the forces moving the boat?

Answer 1

If a boat is going East at 15mph and there is a water current going southeast at 45° then the boat is being drifted southward.  So since the current is going at an angle then it has a x and y component.  So Rx refers to the x-component force of the current and Ry refers to the y-component of the current, and |R| refers to the magnitude of these forces.

Answer 2

Answer:

The boat velocity is 20.6 mph and  14 south of east

Explanation:

For this exercise it is best to write the speeds based on its components x and y

Boat    V1x = 15 mph

Water  V2 = 7.1 mph

           θ = - 45º

 Where the angle is measured from the x axis, the negative indicates that it is measured on an hourly basis

           V2x = V2 cos (-45) = 7.1 (0.707)

           V2y = V2 sin (-45) = 7.1 (-0.707)

           V2x = 5.0 mph

           V2y = -5.0 mph

The total system speed is the sum of each component

          Vx = V1x + V2x

          Vy = V1y + V2y

          Vx = 15 + 5.0

          Vy = 0 -5

          Vx = 20 mph

          Vy = -5.0 mph

We can give result in the form of magnitude and angle

          V² = Vx² + Vy²

          θ = tan-1 (Vy / Vx)

          V = √ [20² ++ (-5)²]

          θ = tan-1 (-5/20)

         

         V = 20.6 mph

         θ = -14º

 The boat velocity is 20.6 mph and  14 south of east