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?

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

force is based upon mass and acceleration.the statement is not always true.

it can be explained from newton's second law of motion.

as per newton's second law of motion the rate of change of momentum is directly proportional to the applied force and takes place along the direction of force.

mathematically it can be written as -

                                              ⇒      

here   k is the proportionality constant whose value is 1.

                                                            [a is the acceleration=dv/dt]

hence we see that force not only depends on mass and acceleration but also on velocity and rate of change of mass. force f will depend on mass and acceleration only when mass is constant.

hence the statement that force is based upon mass and acceleration is false.