A hiker walks 14.7 km at an angle 35o East of South. Find the
East and North components of this walk
To find the East and North components of the walk, we need to break down the distance traveled into its horizontal (East) and vertical (North) components.
Given:
Distance traveled = 14.7 km
Angle = 35o East of South
To find the East component, we need to find the projection of the distance traveled onto the East direction. The angle of 35o East of South means that the angle between the direction of travel and the East direction is 90o - 35o = 55o.
Using trigonometry, we can find the East component as:
East component = Distance traveled * cos(angle)
East component = 14.7 km * cos(55o)
To find the North component, we need to find the projection of the distance traveled onto the North direction. The angle of 35o East of South means that the angle between the direction of travel and the North direction is 35o.
Using trigonometry, we can find the North component as:
North component = Distance traveled * sin(angle)
North component = 14.7 km * sin(35o)
Calculating these values, we get:
East component ≈ 14.7 km * 0.5736 ≈ 8.426 km
North component ≈ 14.7 km * 0.5736 ≈ 5.296 km
Therefore, the East component of the walk is approximately 8.426 km and the North component is approximately 5.296 km.