Chapter 3 Describing Movement in Two Dimensions, 2-D Linear Kinematics
Chapter 3 Describing Movement in Two Dimensions, 2-D Linear Kinematics
Problems & Exercises
3.2 Adding and Subtracting Vectors: Graphical
Use graphical methods to solve these problems. You may assume data taken from graphs is accurate to three digits.
- Find the following for path A in the figure:
(a) the total distance traveled, and
(b) the magnitude and direction of the displacement from start to finish.
The various lines represent paths taken by different people walking in a city. All blocks are 120 m on a side.
Solution: (a) 480 m; (b) 379 m, 18.4º east of north - Find the following for path B in thee figure above:
(a) the total distance traveled, and
(b) the magnitude and direction of the displacement from start to finish.
Solution: (a) 1200m; b) 379m, 18.4º east of north (or 71.6º north of east) - Suppose you walk 18.0 m straight west and then 25.0 m straight north. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements [latex]\mathbf{A}[/latex] and [latex]\mathbf{B}[/latex], then this problem asks you to find their sum [latex]\mathbf{R}=\mathbf{A}+\mathbf{B}[/latex].)
Solution: 30.8m away from the starting point at a direction of 54.3º north of west - Suppose you first walk 12.0 m in a direction 20º west of north and then 20.0 m in a direction 40.0º south of west. How far are you from your starting point, and what is the compass direction of a line connecting your starting point to your final position? (If you represent the two legs of the walk as vector displacements [latex]\mathbf{A}[/latex] and [latex]\mathbf{B}[/latex], then this problem asks you to find their sum [latex]\mathbf{R}=\mathbf{A}+\mathbf{B}[/latex].)
Solution: 19.5 m, 4.65º south of west - Repeat the problem above, but reverse the order of the two legs of the walk; show that you get the same final result. That is, you first walk leg [latex]\mathbf{B}[/latex], which is 20.0 m in a direction exactly 40º south of west, and then leg [latex]\mathbf{A}[/latex], which is 12.0 m in a direction exactly 20º west of north. (This problem shows that [latex]\mathbf{A}+\mathbf{B}=\mathbf{B}+\mathbf{A}[/latex].)
(a) Repeat the problem two problems prior, but for the second leg you walk 20.0 m in a direction 40.0º north of east (which is equivalent to subtracting [latex]\mathbf{\text{B}}[/latex] from [latex]\mathbf{A}[/latex] —that is, to finding [latex]\mathbf{\text{R}}\prime =\mathbf{\text{A}}-\mathbf{\text{B}}[/latex]).
(b) Repeat the problem two problems prior, but now you first walk 20.0 m in a direction 40.0º south of west and then 12.0 m in a direction 20.0º east of south (which is equivalent to subtracting [latex]\mathbf{\text{A}}[/latex] from [latex]\mathbf{\text{B}}[/latex] —that is, to finding [latex]). Show that this is the case. Solution: (a) 26.6 m, 65.1º north of east; (b) 26.6 m, 65.1º south of west - Show that the order of