Question

(9%) Problem 4: Suppose you first walk 11.5 m in a direction 20° west of north and then 27 m in a direction 40° south of west as shown in the figure.

Answer both parts please

Answer 1

35.71 m.

Step-by-step explanation:

There are two ways to solve this problem:

1. Using vector addition:

The first step is to convert the two direction angles (20° and 40°) into their x and y components using the tangent function. We have:

* x_component_first_step = 11.5 m * cos(20°),

* y_component_first_step = 11.5 m * sin(20°),

* x_component_second_step = 27 m * cos(40°),

* y_component_second_step = 27 m * sin(40°).

* Then, we can find the total distance traveled using the Pythagorean theorem:

* total_distance = sqrt((x_component_first_step + x_component_second_step)^2 + (y_component_first_step + y_component_second_step)^2).

2. Using the law of cosines:

We can use the law of cosines to find the total distance, which is given by:

* distance = sqrt[a^2 + b^2 - 2ab cos(alpha)],

* where a and b are the lengths of the two vector components (11.5 m for the first step and 27 m for the second step), and alpha is the angle between the vectors (alpha = 160° - 40°) = 120°.

* So, the distance traveled = sqrt[11.5^2 + 27^2 - 2(11.5)(27)cos(120°)], which gives the total distance of 35.71 m.

Therefore, the total distance traveled by the walker is 35.71 m.