Chapter 3, Problem 4P

Graphically determine the resultant of the following three vector displacements: (1) 24 m, 36° north of east; (2) 18 m, 37° east of north; and (3) 26 m, 33° west of south.

Solution

Resultant vectorof three vector displacements.

Solution: ${\text{19 m, 23}}^{\text{o}}$ North of East

Explanation:

Given:(1) $\text{24 m, 36}˚$ North of East; (2) $\text{18 m, 37}˚$ East of North; (3) $\text{26 m, 33}˚$ West of South.

Graphically, to find the result vector of three vector displacements given in our question we must establish an equivalent scale.In this case, we will take the scale 1cm = 10 m. In this way we start with the first displacement vector: 24 m (2.4 cm in our scale), $36°$ North of East:

  

Then, for the following displacement vector: $\text{18 m, 37}˚$ East of North; the end of the first vector must be joined to the origin of the second as follows:

  

Now, for the third displacement vector: $\text{26 m, 33}˚$ West of South; the end of the second vector must be joined to the origin of the third vector as follows:

  

Finally, to find the displacement vector, the origin of the system is linked to the end of the third displacement vector. The direction is measured with a protractor while its magnitude is measured with the rule, therefore:

  

The resultant vector of three vector displacements is ${\text{19 m, 23}}^{\text{o}}$ North of East.