Learning Introductory Physics with Activities

In the following figure, the magnitudes of the vectors are $|\overrightarrow{a}|=8$ and $|\overrightarrow{b}|=4.5\text{.}$ Assume that $\overrightarrow{c}=\overrightarrow{a}+\overrightarrow{b}$ and $\overrightarrow{d}=\overrightarrow{a}-\overrightarrow{b}\text{.}$

Determine the magnitude of the vectors $\overrightarrow{c}$ and $\overrightarrow{d}\text{?}$ What is the angle to each vector from the positive $x$-axis?

In the following figure, the magnitudes of the vectors are $|\overrightarrow{a}|=5$ and $|\overrightarrow{b}|=5\text{.}$ Assume that $\overrightarrow{c}=\overrightarrow{a}+\overrightarrow{b}$ and $\overrightarrow{d}=\overrightarrow{a}-\overrightarrow{b}\text{.}$

Determine the magnitude of the vectors $\overrightarrow{c}$ and $\overrightarrow{d}\text{?}$ What is the angle to each vector from the positive $x$-axis?

Three vectors add together to equal $0\text{.}$  One vector has magnitude $3$ and points in the positive $x$-direction; a second vector has magnitude $5$ and points at ${120}^o$ from the positive $x$-axis. Determine the third vector as a magnitude and direction.

Use the figure to determine a single vector that is equivalent to the given summation of vectors in each of the cases below.  (The notation $\overrightarrow{PQ}$ represents a vector pointing from point $P$ to point $Q\text{.}$)

A kicker punts a football from the very center of the field to the sideline $42$ yards downfield.  What is the magnitude of the net displacement of the ball in yards?

A certain flying saucer is initially located at a position ${\overrightarrow{r}}_i=400\hat{x}+350\hat{y}\mathrm{m}\text{.}$  After a few minutes it has moved to a location ${\overrightarrow{r}}_f=650\hat{x}-800\hat{y}\mathrm{m}\text{.}$  What is the displacement of the flying saucer? 

A park has a circular pond with a radius of $100\mathrm{m}\text{.}$  Benny starts at its westernmost point, then waddles counterclockwise around the pond until he is at its northernmost point.  What is the magnitude and direction of Benny’s change in position?