A lorry travels 10km northward, 4km eastward,6km southward and 4km westward to arrive at a point T , what is the total displacement?

Answer 1

To find the total displacement of the lorry, we can break down its journey into components and then determine its overall change in position.

1. Break down the movements:

   • The lorry travels 10 km north.
   • Then, it moves 6 km south, which means the net movement in the north-south direction is \(10 - 6 = 4\) km north.
   • Next, it travels 4 km east.
   • Finally, it moves 4 km west, resulting in a net movement in the east-west direction of \(4 - 4 = 0\) km.

2. Resultant displacement:

   • The net movement in the north-south direction is 4 km north.
   • The net movement in the east-west direction is 0 km.

Since the east-west component is zero, the total displacement is simply in the north direction:

\[ \text{Total Displacement} = 4 \text{ km north} \]

3. Magnitude of displacement: To find the magnitude of the total displacement, we can apply the Pythagorean theorem:

\[ \text{Displacement} = \sqrt{(4 \text{ km})^2 + (0 \text{ km})^2} = \sqrt{16} = 4 \text{ km} \]

Thus, the total displacement of the lorry is 4 km north.