A hiker leaves for camp and walked 3.5 KM in a direction of 55 south of West to the lake. After a short rest at the lake she has 2.7 KM in a direction of 16 used to sell to the scenic overlook
5.6 Km
77 degrees south of west
Fred is correct :)
To find the total displacement of the hiker, we can combine the two displacements: the distance and direction from the starting point to the lake, and the distance and direction from the lake to the scenic overlook.
First, let's consider the displacement from the starting point to the lake. The hiker traveled 3.5 km in a direction of 55° south of west. To calculate the horizontal and vertical components of this displacement, we'll use trigonometry.
The horizontal component can be found using the cosine function:
cos(55°) = adjacent/hypotenuse
Let's call the horizontal component "x".
cos(55°) = x/3.5 km
Solving for x, we get:
x = 3.5 km * cos(55°)
Next, let's find the vertical component using the sine function:
sin(55°) = opposite/hypotenuse
We'll call the vertical component "y".
sin(55°) = y/3.5 km
Solving for y, we get:
y = 3.5 km * sin(55°)
So, the displacement from the starting point to the lake is (x, y), where x is the horizontal component and y is the vertical component.
Now, let's consider the displacement from the lake to the scenic overlook. The hiker traveled 2.7 km in a direction of 16°. Again, we'll use trigonometry to find the horizontal and vertical components.
The horizontal component can be found using the cosine function:
cos(16°) = adjacent/hypotenuse
Let's call the horizontal component "x2".
cos(16°) = x2/2.7 km
Solving for x2, we get:
x2 = 2.7 km * cos(16°)
Next, let's find the vertical component using the sine function:
sin(16°) = opposite/hypotenuse
We'll call the vertical component "y2".
sin(16°) = y2/2.7 km
Solving for y2, we get:
y2 = 2.7 km * sin(16°)
So, the displacement from the lake to the scenic overlook is (x2, y2), where x2 is the horizontal component and y2 is the vertical component.
To find the total displacement, we simply add the horizontal and vertical components together:
Total horizontal displacement = x + x2
Total vertical displacement = y + y2
Therefore, the total displacement is (x + x2, y + y2), which represents the final position of the hiker after traveling from the starting point to the lake and then to the scenic overlook.
Huh?
so she ends up z km from camp, where
z^2 = 3.5^2 + 2.7^2 - 2(3.5)(2.7) cos(55-16)°
z = 2.2 km
oops. I had her going S55W, rather than W55S.
z^2 = 3.5^2 + 2.7^2 - 2(3.5)(2.7) cos(25-16)°