# Two crewmen pull a boat through a lock. One crewman pulls with a force of 130 N at an angle of 35 degrees relative to the forward direction of the boat. The second crewman, on the opposite side of...

Two crewmen pull a boat through a lock. One crewman pulls with a force of 130 N at an angle of 35 degrees relative to the forward direction of the boat. The second crewman, on the opposite side of the lock, pulls at an angle for 45 degrees. With what force should the second crewman pull so that the net force of the two crewmen is in the forward direction?

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Two crewmen pull a boat through a lock. The first pulls with a force of 130 N at an angle of 35 degrees relative to the forward direction of the boat.

The force of 130 N applied by the crewman can be divided into its components, one in the forward direction of the boat that is equal to 130*cos 35 and the other in a perpendicular direction equal to 130*sin 35. If the force applied by the second crewman is F, it can be divided into its components, F*cos 45 in the forward direction of the boat and F*sin 45 in a perpendicular direction.

If the net force of the two should be only in the forward direction, the components F*sin 45 and 130*sin 35 should be equal.

F*sin 45 = 130*sin 35

=> `F = 130*(sin 35/sin 45)`

=> `F ~~ 104.45`

The second crewman should apply a force of 104.45 N.

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Let the force applied by the two crewmen be F1 and F2 respectively. For the two forces to balance the the forces in direction perpendicular to the forward direction

F1.sin(45) = F2.sin(35)

F2 = F1.sin(45)/sin(35)

=> F2 = 130.sin(45)/sin(35) = 160.26 N

The second crewman should pull with a force of 160.26 N so that the net force is in the forward direction.

the force = 160.26 N