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The equation shown above in figure c must be used

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Unformatted text preview: of the original displacement vector. This is validated by the formula referenced in question #1. 4. What are the equations for your displacement vectors r11 r12 r21 r22 in unit vector notation? 11= 7.45î + 12.9 11= 14.9, r11x= 7.45, r11y= 12.9 r12= 41.7, r12x=39.88, r12y=12.19 r12= 39.88î + 12.19 r21= 28.5, r21x= 9.74, r21y= 26.78 r21= 9.74î + 26.78 r22= 44, r22x=25.24, r22y=36.04 r22= 25.24î + 36.04 5. If you add the x and y components of any individual vector together, do they represent the vector itself? Can you show this using the pegboard map? The values of the x and y components can be used to derive the value of the vector itself, but not by simply adding them together. The squares of each component must be added together, and then the square root must be taken in order to obtain the magnitude of the vector. The equation shown above in figure c must be used. Also, adding the x and y components will not give the angle at which the vector lies. The formula in figure c for the angle must be used in order to represent the vector completely. This idea can be demonstrated on the pegboard because the components, when aligned tail to head on the pegboard, form a right triangle. The hypotenuse of the triangle formed is the resultant vector, which in this case equals the displacement vectors we have measured. By showing this on the pegboard, one can understand why the Pythagorean theorem is used to compute the value of the displacement vector from its x and y components. 6 6. Are the components of the vector enough to describe the vector itself? What else could be necessary? A vector consists of a magnitude and a direction, so just the components of the vector do not describe the vector it self. You would also need the angle at wh ich the it was directed in order to fully describe the vector. 7. Can you use the vector information you collected to determine the Verify your answers using the pegboard map. Yes, it is possible to determine the displacement vectors between Start 1, Start 2 and End 1, End 2. To calculate start 1 to start 2, the vector path components 11 21 must be added together and used in the figure c formula. To calculate End 1 to End 2, the vector path components from 12 22 must be added together and used in the formula as well. By adding these components together, a path is made from Start 1 to Start 2 and from End 1 to End 2, respectively. It is possible to calculate this because we have already gathered all of those values. 8. What do you t...
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