A person walks 11.2 ◦ north of east for 4.06 km. Another person walks due north, then due east to arrive at the same location. How far due north would this person walk? Answer in units of km
what is 4.06* cos11.2 ?
To find out how far the second person would walk due north, we need to determine the displacement of the first person's walk.
The displacement is a straight line measure from the initial point to the final point. We can calculate it using the concept of vector addition.
The first person walks 11.2° north of east for 4.06 km. To find the northward component of their walk, we need to resolve the displacement into its northward and eastward components.
1. Calculate the eastward component:
eastward_component = displacement * cos(angle)
= 4.06 km * cos(11.2°)
2. Calculate the northward component:
northward_component = displacement * sin(angle)
= 4.06 km * sin(11.2°)
Now, let's find the second person's distance due north.
Since the second person walks due north and then due east, the northward component of their walk is the same as the northward component of the first person's walk.
northward_distance_second_person = northward_component
So, to find the distance due north that the second person walks, we substitute the calculated value of the northward component, which is 4.06 km * sin(11.2°), into the equation.
northward_distance_second_person = 4.06 km * sin(11.2°)
Calculate the expression to find the numerical value of the northward distance traveled by the second person.
northward_distance_second_person = 4.06 km * sin(11.2°)
northward_distance_second_person ≈ 0.823 km
Therefore, the second person would walk approximately 0.823 km due north.