Barge Pulled by Tugboats#

A barge is pulled by the two tugboats shown in the following figure. One tugboat pulls on the barge with a force of magnitude $$F_2 =$$ 5230 units of force at $$\theta_2 =$$ 23$$^{\circ}$$ above the line AB and the other tugboat pulls on the barge with a force of magnitude $$F_1 =$$ 3512 units of force at $$\theta_1 =$$ 13$$^{\circ}$$ below the line AB.

Assume $$+y$$ is straight ahead, and $$+x$$ is to the right.

Figure of a barge pulled by two tugboats.
A straight line AB is drawn through the center of the barge. One tugboat pulls the barge to the left with a force of magnitude $F_1$ at an angle $\theta_1$ relative to AB. The other tugboat pulls to the right with a force $F_2$ at angle $\theta_2$ relative to AB.

Part 1#

Resolve the pulling forces to their components. What is the $$x$$-component of the right-force (i.e. $$F_2$$)? Remember to consider the sign convention.

Please enter in a numeric value in â€˜units of forceâ€™.

Part 2#

Resolve the pulling forces to their components. What is the $$y$$-component of the right-force (i.e. $$F_2$$)? Remember to consider the sign convention.

Please enter in a numeric value in â€˜units of forceâ€™.

Part 3#

Resolve the pulling forces to their components. What is the $$x$$-component of the left-force (i.e. $$F_1$$)? Remember to consider the sign convention.

Please enter in a numeric value in â€˜units of forceâ€™.

Part 4#

Resolve the pulling forces to their components. What is the $$y$$-component of the left-force (i.e. $$F_1$$)? Remember to consider the sign convention.

Please enter in a numeric value in â€˜units of forceâ€™.

Part 5#

What is the magnitude of the resultant pull?

Please enter in a numeric value in â€˜units of forceâ€™.

Part 6#

What is the direction of the resultant vector relative to the line AB?

• 8.65$$^{\circ}$$ to the right of AB.

• 8.65$$^{\circ}$$ to the left of AB.

• 81.3$$^{\circ}$$ to the right of AB.

• 81.3$$^{\circ}$$ to the left of AB.

• 86.5$$^{\circ}$$ to the right of AB.

• 86.5$$^{\circ}$$ to the left of AB.