Respuesta :
Answer:
The final displacement from the origin is 1.6 km to the NE
Explanation:
The directions in which the delivery truck travels are;
1) 2.8 km North = 2.8·[tex]\hat j[/tex], in vector form
2) 1.0 km East = 1.0·[tex]\hat i[/tex], in vector form
3) 1.6 km South = -1.6·[tex]\hat j[/tex], in vector form
Therefore, to find the final displacement, Δx, of the delivery truck, we add the individual displacements as follows;
Final displacement, Δd = 2.8·[tex]\hat j[/tex] + 1.0·[tex]\hat i[/tex] +(-1.6·[tex]\hat j[/tex]) = 1.2·[tex]\hat j[/tex] + 1.0·[tex]\hat i[/tex]
Final displacement, = 1.0·[tex]\hat i[/tex] + 1.2·[tex]\hat j[/tex]
Where;
Δx = The displacement in the x-direction = 1.0·[tex]\hat i[/tex]
Δy = The displacement in the y-direction = 1.2·[tex]\hat j[/tex]
The magnitude of the resultant displacement vector is given as follows
[tex]\left | d \right |[/tex] = √((Δx)² + (Δy)²) = √(1² + 1.2²) ≈ 1.6 (To the nearest tenth)
The magnitude of the resultant displacement vector ≈ 1.6 km
The direction of the resultant vector is positive for both the east and north direction, therefore, the direction of the resultant vector = NE
Therefore, the resultant displacement of the delivery truck is approximately 1.6 km, NE from the origin.
