A man walks 40 meters north and turns and walks 60 meters in a direction 30 degrees to the east of north.
What is the distance traveled?
What is his displacement?
Figure the E and N components fo the second walk,then add as vectors to the original N walk.
distance of course is 100m.
diplacement is the resultant vector.
what is the resultant vector? I don't understand.
Break the sixty meter into components:
http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html#vec5
then add the original N walk, then find the resultant displacement.
http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html#vec7
Is a Chiropractic a Physican specializing in allergies?
To find the distance traveled, we need to calculate the total distance covered by the man.
In this scenario, the man walks 40 meters north and then turns and walks 60 meters in a direction 30 degrees east of north.
To calculate the distance traveled:
1. We start by finding the horizontal distance traveled eastwards, which can be determined using the cosine function since the direction is given relative to the north.
Eastward distance = 60 meters * cos(30 degrees)
Eastward distance = 60 meters * (√3/2)
Eastward distance ≈ 52.1 meters
2. Next, we need to find the vertical distance traveled northwards, which can be calculated using the sine function.
Northward distance = 40 meters * sin(30 degrees)
Northward distance = 40 meters * (1/2)
Northward distance = 20 meters
3. Finally, we can determine the total distance traveled by adding the eastward and northward distances.
Total Distance = Eastward distance + Northward distance
Total Distance = 52.1 meters + 20 meters
Total Distance ≈ 72.1 meters
Therefore, the distance traveled by the man is approximately 72.1 meters.
To find the displacement, we need to calculate the straight-line distance and direction from the starting point to the endpoint. The displacement is a vector quantity and it represents the shortest straight-line path between the starting and ending points.
To calculate the displacement:
1. We can combine the horizontal and vertical distances to find the resultant displacement.
Resultant Displacement = √[(Eastward distance)^2 + (Northward distance)^2]
Resultant Displacement = √[(52.1 meters)^2 + (20 meters)^2]
Resultant Displacement ≈ √[2714.41 + 400]
Resultant Displacement ≈ √3114.41
Resultant Displacement ≈ 55.81 meters
2. We also need to determine the direction of the displacement. The direction can be found by taking the inverse tangent of the ratio of the northward distance to the eastward distance.
Displacement Direction = arctan(Northward distance / Eastward distance)
Displacement Direction = arctan(20 meters / 52.1 meters)
Displacement Direction ≈ 21.8 degrees
Therefore, the displacement of the man is approximately 55.81 meters in a direction 21.8 degrees east of north.