Vector Displacement| Vector Addition and Subtraction: Graphical Method| Two-Dimensional Kinematics| College Physics Problem 3.7

(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 B from A —that is, to finding R′ =A−B ). (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 A from B —that is, to finding R′′ = B - A = - R′ ). Show that this is the case.

Vector Displacement| Vector Addition and Subtraction: Graphical Method| Two-Dimensional Kinematics| College Physics Problem 3.6

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 B , which is 20.0 m in a direction exactly 40º south of west, and then leg A , which is 12.0 m in a direction exactly 20º west of north. (This problem shows that A+B=B+A.)

Vector Displacement| Vector Addition and Subtraction: Graphical Method| Two-Dimensional Kinematics| College Physics Problem 3.5

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 A and B , as in Figure 3.56, then this problem finds their sum R=A+B.)

Vector Displacement| Vector Addition and Subtraction: Graphical Method| Two-Dimensional Kinematics| College Physics Problem 3.4

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 A and B, as in Figure 3.55, then this problem asks you to find their sum R = A + B .)

Displacement| Vector Addition and Subtraction: Graphical Method| Two-Dimensional Kinematics| College Physics Problem 3.3

Find the north and east components of the displacement for the hikers shown in Figure 3.52.

Distance vs Displacement| Vector Addition and Subtraction: Graphical Method| Two-Dimensional Kinematics| College Physics Problem 3.2

Find the following for path B in Figure 3.54: (a) the total distance traveled, and (b) the magnitude and direction of the displacement from start to finish.

Distance vs Displacement| Vector Addition and Subtraction: Graphical Method| Two-Dimensional Kinematics| College Physics Problem 3.1

Find the following for path A in Figure 3.54: (a) the total distance traveled, and (b) the magnitude and direction of the displacement from start to finish.

College Physics Problem 2.29

Freight trains can produce only relatively small accelerations and decelerations. (a) What is the final velocity of a freight train that accelerates at a rate of \$latex 0.0500\:m/s^2&s=1&fg=000000\$ for 8.00 minutes, starting with an initial velocity of 4.00 m/s? (b) If the train can slow down at a rate of \$latex 0.550\:m/s&s=1&fg=000000\$, how long will it take to … Continue reading College Physics Problem 2.29

College Physics Problem 2.4

Find the following for path D in the figure: (a) The distance traveled. (b) The magnitude of the displacement from start to finish. (c) The displacement from start to finish.    SOLUTION: a) The distance is b) The displacement is c) The displacement is

College Physics Problem 2.3

Find the following for path C in the figure: (a) The distance traveled. (b) The magnitude of the displacement from start to finish. (c) The displacement from start to finish. SOLUTION: a) The distance is the sum of all the paths of C. b) The magnitude is the difference between the final position and the … Continue reading College Physics Problem 2.3