How do I answerthis physics problem with sum of the forces?

Question

Threeconstruction workers wish to pull a cement mixer due East, as shownin the top-view illustration below. The first worker W1 pulls witha force of 100 N at an angle of 60 degrees North of East, while asecond worker W2 pulls with a force of 80 N at an angle of 30degrees South of East. Determine the smallest force (both magnitudeand direction) that the third worker must exert to permit thecement mixer to move due east.

I think the direction is 270 degrees based on my drawing. I triedsum of the forces in the y direction an got 46.6 N for W3, but I'mnot sure if this is the correct answer. Also, do I need to show anywork for the 270 degree direction? Threeconstruction workers wish to pull a cement mixer due East, as shownin the top-view illustration below. The first worker W1 pulls witha force of 100 N at an angle of 60 degrees North of East, while asecond worker W2 pulls with a force of 80 N at an angle of 30degrees South of East. Determine the smallest force (both magnitudeand direction) that the third worker must exert to permit thecement mixer to move due east.

I think the direction is 270 degrees based on my drawing. I triedsum of the forces in the y direction an got 46.6 N for W3, but I'mnot sure if this is the correct answer. Also, do I need to show anywork for the 270 degree direction?

Explanation / Answer

I agree with the result you obtained (for Fy) If the third worker were to pull in any other direction thandirectly South then he would have to pull with a greater force to obtain the samey-component of force.

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