A person walks 10.4 degrees north of east for 4.19km. 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.
D = 4.19*sin10.4 =
To solve this problem, we need to break it down into components. Let's consider the first person's displacement:
1. The person walks 10.4 degrees north of east for 4.19km.
- This means they're walking at an angle of 10.4 degrees measured from the east direction, towards the north.
- We can find the north and east components of this displacement using trigonometry.
To find the north component:
- We can use the cosine function, as the angle is measured from the east direction.
- The north component will be the displacement multiplied by the cosine of the angle.
- Let's calculate it: north component = 4.19 km * cos(10.4 degrees)
To find the east component:
- We can use the sine function, as the angle is measured from the east direction.
- The east component will be the displacement multiplied by the sine of the angle.
- Let's calculate it: east component = 4.19 km * sin(10.4 degrees)
Now, for the second person who walks due north, then due east:
- The displacement is directed purely north for a certain distance, then purely east for another distance.
- Since they arrive at the same location, the north and east components of their displacement should be equal to the components of the first person's displacement.
Since the second person walks purely north, the north component of their displacement will be the same as the north component of the first person's displacement. Therefore, the distance due north that the second person walks is:
north component = 4.19 km * cos(10.4 degrees)
Now, let's calculate it: