## Q. 3.2

CASE STUDY Cassidi Reese’s Displacement

As described previously, Reese opened her parachute when she was directly above a grove of trees, but she landed safely in a nearby field. In Figure 3.12, a reference point has been chosen, and her position $\vec{r}_i$ when she opened the parachute and her position $\vec{r}_f$ when she landed are measured from this reference point. Draw the vector that represents her displacement during this time interval. ## Verified Solution

INTERPRET and ANTICIPATE
According to Equation 3.6, to find her displacement, we subtract her initial position vector $\vec{r}_i$ from her final position vector $\vec{r}_f$. There are two ways to do this step geometrically.

$\Delta \overrightarrow{ r }=\overrightarrow{ r }_f-\overrightarrow{ r }_i \quad \quad (3.6)$

SOLVE
Because the two vectors are already tail to tail, the most convenient subtraction method is tail-to-tail subtraction, in which the displacement vector $\Delta \vec{r}$ points from the head of $\vec{r}_i$ to the head of $\vec{r}_f$ (Fig. 3.13).

CHECK and THINK
Displacement is the change in position, so it makes sense that the displacement vector is an arrow that runs from Reese’s initial position above the trees to her final position on the ground. 