a hiker walks 14.7 km at an angle 35 degrees south of east. Find the east and north components of this walk.
Why did the hiker go south of east? Because they heard the penguins throw an ice cream party down there! 🐧🍦
Now, let's find those components. To break it down, we'll use some trigonometry. The angle south of east forms a right-angled triangle with the east and north components as the legs.
The east component can be found using cosine, which is adjacent over hypotenuse. In this case, the hypotenuse is the 14.7 km walk. So, the east component is:
East = cos(35°) * 14.7 km
The north component can be found using the sine function, which is opposite over hypotenuse. So, the north component becomes:
North = sin(35°) * 14.7 km
After crunching the numbers, you'll find that the east component is approximately 12.01 km (rounded to the nearest hundredth), and the north component is approximately 8.43 km (also rounded to the nearest hundredth).
So, the hiker stumbled upon 12.01 km east and 8.43 km north while chasing after those mischievous penguins! 🚶♂️🐧
To find the east and north components of the hiker's walk, we can use trigonometry.
1. First, let's assume that the hiker starts at the origin (0,0).
2. The hiker walks at an angle of 35 degrees south of east. Since east is considered positive in the x-axis and north is considered positive in the y-axis, this means the hiker is moving in the fourth quadrant.
3. The south of east direction means the angle is measured from the negative x-axis. Therefore, we need to subtract the angle from 180 degrees: 180 - 35 = 145 degrees.
4. Now, using trigonometry, we can find the east and north components.
- The east component is given by: E = distance * cos(angle)
- The north component is given by: N = distance * sin(angle)
- In this case, the distance is given as 14.7 km and the angle is 145 degrees.
5. Let's calculate the east and north components:
E = 14.7 km * cos(145 degrees)
N = 14.7 km * sin(145 degrees)
6. Using a scientific calculator or trigonometric tables, we can find the cosine and sine values for 145 degrees, which are approximately -0.5736 and 0.8192, respectively.
7. Calculating the east and north components:
E ≈ 14.7 km * (-0.5736) ≈ -8.42 km (rounded to two decimal places)
N ≈ 14.7 km * 0.8192 ≈ 12.03 km (rounded to two decimal places)
So, the east component of the walk is approximately -8.42 km, and the north component of the walk is approximately 12.03 km.
To find the east and north components of the walk, we need to use trigonometry formulas. The east component represents the distance traveled in the eastward direction, and the north component represents the distance traveled in the northward direction.
Given that the hiker walks 14.7 km at an angle 35 degrees south of east, let's calculate the east and north components step by step:
1. East Component:
To find the east component, we need to determine the distance traveled in the eastward direction. We can use the trigonometric function cosine (cos) to calculate it.
East Component = 14.7 km * cos(35 degrees)
2. North Component:
To find the north component, we need to determine the distance traveled in the northward direction. Since the hiker is walking south of east, the northward component will be in the negative direction. We can use the trigonometric function sine (sin) to calculate it.
North Component = -14.7 km * sin(35 degrees)
Now, let's calculate the east and north components:
East Component = 14.7 km * cos(35 degrees)
= 14.7 km * 0.819 (rounded to three decimal places)
≈ 12.051 km
North Component = -14.7 km * sin(35 degrees)
= -14.7 km * (-0.574) (rounded to three decimal places)
≈ 8.419 km
So, the east component of the walk is approximately 12.051 km, and the north component is approximately 8.419 km.
Vector: 14.7km @ (-35)deg = 325deg CCW,
4th QUAD.
X = hor = 14.7*cos(325)=12.04km = East Comp.
Y = ver = 14.7*sin(325) = -8.43km = South Comp.