Resultant displacment and magnitude

[djtsmith007]

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

 

[mikelepore]

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.

 

[tomcue]

Your attempt at using the equation was a good start. However, you have made a few mistakes in setting up the equation.

Firstly, the equation you provided is for the law of cosines, which is used to find the magnitude of the resultant displacement when given the magnitudes and angles of two displacements. In this case, we are trying to find the magnitude of the second displacement, so we need to use the law of sines.

Secondly, you have set Φ=49⁰, which is the angle of the resultant displacement. However, we need to find the angle of the second displacement, which is not given in the problem. We can use the law of sines to find this angle.

So, the correct setup for the equation would be:

Sin(β)/215 = Sin(131⁰)/235

Solving for Sin(β), we get:

Sin(β) = (215/235) * Sin(131⁰) = 0.919

Now, we can use the law of sines again to find the magnitude of the second displacement:

Sin(β)/X = Sin(49⁰)/215

Solving for X, we get:

X = (215/ Sin(49⁰)) * Sin(β) = (215/0.754) * 0.919 = 251.9 cm

Therefore, the magnitude of the second displacement is 251.9 cm.