Finding the second displacement from the first and resultant

In summary, a particle undergoes two displacements with the first having a magnitude of 147 cm and making an angle of 115 degrees with the positive x axis. The resultant displacement has a magnitude of 188 cm and is directed at an angle of 29.6 degrees to the positive x axis. To find the magnitude and direction of the second displacement, one can use the components of the first and resultant displacements and apply the Pythagorean theorem. This will give the magnitude and direction of the second displacement within the limits of -180 to 180 degrees counterclockwise from the x axis.
  • #1
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Homework Statement



A particle undergoes two displacements. The first has a magnitude of 147 cm and makes an angle of 115 degrees with the positive x axis. The resultant displacement has a magnitude of 188 cm and is directed at an angle of 29.6 degrees to the positive x axis.

a) Find the magnitude of the second displacement.
b) Find the direction of the second displacement (with positive measured counterclockwise from the x axis, between the limits of -180 degrees and 180 degrees).



Homework Equations



Not entirely sure.
Possibly

147{cos115,sin115}

188{cos29.6,sin29.6}



The Attempt at a Solution



I've done similar problems to this (finding the resultant displacement) but I don't know how to find the second displacement. I tried looking this problem up and couldn't find any help that led to the right answer.
 
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  • #2
if you're ok with using just components, then x1+ x2 = xtotal ... gives you x2 since you know x1 and xtotal.
similarly, y1 + y2 = ytotal gives you y2 since you know y1 and ytotal.

Don't forget Pythagoras, if they want magnitudes!
 
  • #3
Thanks!
 

Related to Finding the second displacement from the first and resultant

1. How do I find the second displacement from the first and resultant?

To find the second displacement from the first and resultant, you can use the Pythagorean theorem. First, square the values of the first and resultant displacements. Then, add the two values together. Finally, take the square root of the sum to find the second displacement.

2. Is it necessary to know the direction of the displacements?

Yes, it is necessary to know the direction of the displacements in order to accurately calculate the second displacement. The direction will affect the final value, so make sure to include it in your calculations.

3. Can I use vectors to find the second displacement?

Yes, vectors can be used to find the second displacement from the first and resultant. Vectors represent both magnitude and direction, making them useful for calculating displacements.

4. What if there are more than two displacements?

If there are more than two displacements, you can still use the Pythagorean theorem to find the second displacement. First, calculate the resultant of the first two displacements. Then, use that resultant as the first displacement and repeat the process until you have calculated the second displacement.

5. How can I use this concept in real-world situations?

This concept is commonly used in physics and engineering to calculate the resulting displacement of an object or system. It can also be applied in navigation, such as finding the displacement of a ship or plane after undergoing multiple changes in direction. Additionally, it can be used in sports to determine the distance and direction of a player's movement on the field or court.

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