A hiker walks 17.0 km at an angle 40° south of east. Find the east and north components of this walk
40o S. of E. = 320o CCW.
d = 17km[320o].
X = 17*Cos320 = East component.
Y = 17*sin320 = South component.
No north component.
To find the east and north components of the hiker's walk, we can use trigonometry.
First, let's define our coordinate system. We'll consider east to be the positive x-direction and north to be the positive y-direction.
We have the total distance traveled by the hiker, which is 17.0 km. We also have the angle the hiker is walking relative to the east direction, which is 40° south of east.
To find the east component, we can use the cosine function:
East component = distance * cosine(angle)
East component = 17.0 km * cosine(40°)
To find the north component, we can use the sine function:
North component = distance * sine(angle)
North component = 17.0 km * sine(40°)
Calculating the values:
East component ≈ 17.0 km * cosine(40°) ≈ 17.0 km * 0.766 ≈ 13.022 km
North component ≈ 17.0 km * sine(40°) ≈ 17.0 km * 0.643 ≈ 10.927 km
So, the east component of the hiker's walk is approximately 13.022 km, and the north component is approximately 10.927 km.