A boy walks 100 m north then walks 50 m east and then 80 m south. Calculate the net displacement.
total of 20 north
total of 50 east
magnitude = sqrt (400 +2500)= 10 sqrt 29
tan angle north of east = 2/5 = 0.4
angle n of e = 21.8 deg
To calculate the net displacement, we need to find the vector sum of the individual displacement vectors.
Given:
1. The boy walks 100 m north.
2. The boy walks 50 m east.
3. The boy walks 80 m south.
We can represent these displacements as vectors:
1. North displacement: 100 m (upwards)
2. East displacement: 50 m (to the right)
3. South displacement: 80 m (downwards)
Now, let's represent these vectors on a coordinate plane:
Starting from the origin (0,0), the north displacement vector goes up by 100 units, the east displacement vector goes right by 50 units, and the south displacement vector goes down by 80 units.
To calculate the net displacement, we can sum up the individual displacements:
Net displacement = North displacement + East displacement + South displacement
To simplify the calculation, let's consider the horizontal and vertical components separately:
Horizontal displacement = East displacement = 50 m (to the right)
Vertical displacement = North displacement - South displacement = 100 m - 80 m = 20 m (upwards)
So, the horizontal displacement is 50 m to the right, and the vertical displacement is 20 m upwards.
To find the net displacement, we can use the Pythagorean theorem:
Net displacement = √(Horizontal displacement^2 + Vertical displacement^2)
= √(50^2 + 20^2)
= √(2500 + 400)
= √(2900)
≈ 53.85 m (rounded to two decimal places)
Therefore, the net displacement of the boy is approximately 53.85 m.
To find the net displacement, we need to find the total distance and direction from the starting point to the end point. We can use the Pythagorean theorem to calculate the distance.
First, let's break down the movements:
1. The boy walks 100 m north: This means he moves directly upwards on the vertical axis.
2. Then, he walks 50 m east: This means he moves to the right on the horizontal axis.
3. Finally, he walks 80 m south: This means he moves directly downwards on the vertical axis.
Now, let's calculate the horizontal and vertical components of the displacement:
1. Horizontal component (east/west): Since the boy only moves east, the horizontal component is 50 m to the right.
2. Vertical component (north/south): The boy initially moves 100 m north and then 80 m south. So the vertical component can be calculated as 100 m - 80 m = 20 m to the north.
Now, we can use the Pythagorean theorem to find the magnitude of the displacement:
Displacement = √(horizontal component^2 + vertical component^2)
Displacement = √((50 m)^2 + (20 m)^2)
Displacement = √(2500 m^2 + 400 m^2)
Displacement = √(2900 m^2)
Displacement ≈ 53.85 m
Therefore, the net displacement is approximately 53.85 meters and it is in a northeasterly direction.