Question

A delivery truck travels 2.8 km North, 1.0 km East, and 1.6 km South. The final displacement from the origin is ___km to the ___.(round to the nearest tenth) (write the resultant vector as NE, SE, NW, or SW)

Answer 1

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·$\hat j$, in vector form

2) 1.0 km East = 1.0·$\hat i$, in vector form

3) 1.6 km South = -1.6·$\hat j$, 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·$\hat j$ + 1.0·$\hat i$ +(-1.6·$\hat j$) = 1.2·$\hat j$ + 1.0·$\hat i$

Final displacement, = 1.0·$\hat i$ + 1.2·$\hat j$

Where;

Δx = The displacement in the x-direction = 1.0·$\hat i$

Δy = The displacement in the y-direction = 1.2·$\hat j$

The magnitude of the resultant displacement vector is given as follows

$\left | d \right |$ = √((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.