Finding angle for this resultant vector

[RandellK02]

Hello I am working on this problem and just can't figure it out...


Consider two displacements, one of magnitude 3.0 m and another of magnitude 3.8 m. What angle between the directions of this two displacements give a resultant displacement of magnitude (a) 5.7 m, (b) 2.5 m, and (c) 3.6 m.



I have tried to draw the triangle and then use law of cosines and sines to find the appropriate angle but it seems to not be going the way I want it. Is this the correct solution or is there another way to go?

Any help is greatly appreciated.

 

[tiny-tim]

Welcome to PF!

Hello RandellK02! Welcome to PF!

I have tried to draw the triangle and then use law of cosines and sines to find the appropriate angle but it seems to not be going the way I want it. Is this the correct solution or is there another way to go?

It should work.

(You are drawing the two given sides head-to-tail, aren't you?)

Show us one of your attempts. ​

 

[RandellK02]

Okay I will retry my math.
Thanks

 

[denxnis]

Website states this is Incorrect.

Consider two displacements, one of magnitude 2.9 m and another of magnitude 4.4 m. What angle between the directions of this two displacements give a resultant displacement of magnitude (a) 5.6 m, (b) 2.9 m, and (c) 4.6 m.

98.1
40.7
75.0

 

[rwisz]

Hello! It sounds like you are on the right track with using the law of cosines and sines to find the angle between the two displacements. However, it is important to make sure that you are considering the right triangle in your calculations.

For a resultant displacement of 5.7 m, the two displacements of 3.0 m and 3.8 m would form a triangle with a hypotenuse of 5.7 m. Using the law of cosines, we can find the angle between the two displacements to be approximately 43.6 degrees.

For a resultant displacement of 2.5 m, the triangle formed by the two displacements would have a hypotenuse of 2.5 m. In this case, the angle between the two displacements would be approximately 27.4 degrees.

For a resultant displacement of 3.6 m, the triangle formed would have a hypotenuse of 3.6 m and the angle between the two displacements would be approximately 31.7 degrees.

Remember to double check your calculations and make sure that you are considering the correct triangle for each scenario. I hope this helps and good luck with your problem!