A surveillance report concerning a suspected car details the following: 'The car travelled 2.00 km towards east, executed a perpendicular left turn, proceeded for 500 m , executed a perpendicular right turn, travelled for 4.00 km and halted.' Determine the displacement of the car.

Step-by-step solution

Let the initial position of the car be the origin (0,0) . The car travels 2.00 km towards east, so the first displacement vector is d ₁ = 2.00 i km . A perpendicular left turn from east is towards north. The car travels 500 m = 0.50 km , so the second displacement vector is d ₂ = 0.50 j km . A perpendicular right turn from north is towards east. The car travels 4.00 km , so the third displacement vector is d ₃ = 4.00 i km . The total displacement vector is D = d ₁ + d ₂ + d ₃ = 2.00 i + 0.50 j + 4.00 i = 6.00 i + 0