Question

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.)

In vector addition, reversing the order of two legs in a walk yields the same result. What is the magnitude of the displacement when leg A is walked first and then leg B?
1. 32.0 m
2. 16.0 m
3. 8.0 m
4. 28.0 m

Answer 1

When the order of the two legs of the walk is reversed, the magnitude of the displacement is 8.0 m.

Step-by-step explanation:

To find the final displacement when the order of the two legs of the walk is reversed, we need to add the two legs in the reverse order. First, let's find the vector components of leg B. The horizontal component of leg B is -20.0 m * cos(40°), and the vertical component is -20.0 m * sin(40°). For leg A, the horizontal component is 12.0 m * cos(20°), and the vertical component is 12.0 m * sin(20°).

When we add the components of leg B first and then leg A, we get the horizontal component of the final displacement as -20.0 m * cos(40°) + 12.0 m * cos(20°), and the vertical component as -20.0 m * sin(40°) + 12.0 m * sin(20°). Using these components, we can find the magnitude of the displacement using the Pythagorean theorem: sqrt[(-20.0 m * cos(40°) + 12.0 m * cos(20°))^2 + (-20.0 m * sin(40°) + 12.0 m * sin(20°))^2]. Calculating the value, we get 8.0 m (option 3).