How Do You Calculate the Second Vector in a Vector Displacement Problem?

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To calculate the second vector in a vector displacement problem, first, understand that the resultant vector is derived from the sum of the two individual vectors. Given the first vector's magnitude of 150 cm at 120 degrees and the resultant vector's magnitude of 140 cm at 35 degrees, the second vector can be determined by vector component addition. The approach involves breaking down the vectors into their x and y components, then using these components to solve for the unknown second vector. The discussion highlights the importance of understanding vector addition and the relationships between the vectors involved. Solving for the second vector requires careful application of trigonometric functions and vector principles.
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Homework Statement


A man pushing a mop across a floor causes the mop to undergo two displacements. The first has a magnitude of 150 cm and makes an angle of 120 degrees with the positive x axis. The resultant displacement has a magnitude of 140 cm and is directed at an angle of 35 degrees to the positive x axis. Find the magnitude and direction of the second displacement (second vector)


Homework Equations



Vector Component Addition

The Attempt at a Solution


I realize that somehow, we know the resultant vector and one of the vectors and need to solve for the second vector. Because nothing is known about the second vector, I don't know how to go about that. I've been working on this problem all day and truly need some help.
 
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Hi singingblonde.

Suppose for a moment that the problem was reversed: the two vectors were given (for example: 150 cm with an angle of 120 degrees with the x-axis, and 140 cm at an angle of 35 degrees to the x-axis) and you were asked to calculate the resultant vector. Would you know how to solve that?
 

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