a man runs for 6km directly to the east until he gets to a T Junction where he turns around for another 8km directly west .
determine the total displacement of the man.
To determine the total displacement of the man, we need to consider both the distance he traveled and the direction he traveled in.
The man initially runs 6km directly to the east. This means he is moving in the positive x-direction.
After reaching the T-junction, he turns around and runs 8km directly west. This means he is moving in the negative x-direction.
The displacement is the overall change in position from the starting point to the ending point. In this case, the starting point is the origin (0,0) and the ending point is the point where the man stops after running west.
Since the man initially runs 6km to the east (positive x-direction), his position at that point would be (6,0).
When he turns around and runs 8km west (negative x-direction), his position would be (6-8, 0) which simplifies to (-2, 0).
The total displacement, which represents the overall change in position, can be found by subtracting the initial position (6,0) from the final position (-2,0):
Total Displacement = (-2,0) - (6,0) = (-8, 0)
Therefore, the total displacement of the man is -8km, in the west (-x) direction.