A man walks 5km due north and 12km due south determine his resultant displacement in magnitude and direction
I would draw the triangle and determine the angle (direction) and hypotenuse (magnitude).
To determine the resultant displacement of the man, we can calculate the net distance traveled in both the north and south directions, and then calculate the magnitude and direction of the resultant displacement.
Step 1: Calculate the net distance traveled in the north direction:
The man walks 5km due north, so the net distance traveled in the north direction is 5km.
Step 2: Calculate the net distance traveled in the south direction:
The man walks 12km due south, so the net distance traveled in the south direction is 12km.
Step 3: Calculate the magnitude of the resultant displacement:
The magnitude of the resultant displacement is given by the difference between the net distances traveled in the north and south directions. In this case, it is calculated as follows:
Magnitude = |Net distance north - Net distance south| = |5km - 12km| = |-7km| = 7km
Step 4: Determine the direction of the resultant displacement:
The direction of the resultant displacement is determined by the net distance traveled in the north and south directions. In this case, since the net distance traveled in the south direction is greater, the resultant displacement is directed south.
Therefore, the resultant displacement of the man is 7km due south.
To determine the resultant displacement in magnitude and direction, we can visualize the man's movements on a coordinate plane. Let's assume the starting point is the origin (0,0).
First, the man walks 5 km due north, which means he moves 5 km in the positive y-direction. This can be represented as a vector (0, 5).
Then, the man walks 12 km due south, which means he moves 12 km in the negative y-direction. This can be represented as a vector (0, -12).
To calculate the resultant displacement, we need to add these two vectors. We can simply add their respective components:
x-component: 0 + 0 = 0
y-component: 5 + (-12) = -7
Therefore, the resultant displacement is (0, -7). The magnitude of this displacement can be found using the Pythagorean theorem:
Magnitude = √(0^2 + (-7)^2) = √(0 + 49) = √49 = 7 km
So, the man's resultant displacement is 7 km and it points in the negative y-direction, which is south.