Resultant displacment and magnitude

AI Thread Summary
The discussion revolves around calculating the magnitude of a second displacement after a man pushes a mop, resulting in two displacements. The first displacement is 235 cm at an angle of 131° with the positive x-axis, while the resultant displacement is 215 cm at an angle of 49°. The participant is struggling to apply the formula R=√(A²+B²-2AB(cos(Φ)) and seeks clarification on their approach. They are advised to find the x and y components of both displacements and use vector subtraction to determine the second displacement. The conversation emphasizes the importance of correctly breaking down the vector components for accurate calculations.
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Homework Statement


A man pushes a mop across the floor causes the mop to undergo two displacements. The first has a magnitude of 235cm and makes an angle of 131⁰ with the positive x-axis.

The resultant displacement has a magnitude of 215cm and is directed at an angle of 49⁰ to the positive x-axis.

Find the magnitude of the second displacement. Answer in units of cm.

Homework Equations



R=√(Aˆ2+Bˆ2-2AB(cos(Φ)))

Sinβ=B/R(Sin(Φ))

The Attempt at a Solution



Tried using the above equation and not getting the right answer.
What am i doing wrong?
I set
R=215
A=235
B=X second displacement
Φ=49⁰
 
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A+B=R implies B=R-A. Find the x and y components of R and A, then recall how to subtract two vectors when you know their components.
 
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