4.1 Displacement and velocity vectors  (Page 4/7)

What form does the trajectory of a particle have if the distance from any point A to point B is equal to the magnitude of the displacement from A to B ?

Give an example of a trajectory in two or three dimensions caused by independent perpendicular motions.

If the instantaneous velocity is zero, what can be said about the slope of the position function?

The coordinates of a particle in a rectangular coordinate system are (1.0, –4.0, 6.0). What is the position vector of the particle?

The position of a particle changes from ${\overrightarrow{r}}_1=(2.0\text{}\widehat{i}+3.0\widehat{j})\text{cm}$ to ${\overrightarrow{r}}_2=(\mathrm{-4.0}\widehat{i}+3.0\widehat{j})\text{cm}.$ What is the particle’s displacement?

The 18th hole at Pebble Beach Golf Course is a dogleg to the left of length 496.0 m. The fairway off the tee is taken to be the x direction. A golfer hits his tee shot a distance of 300.0 m, corresponding to a displacement $\text{Δ}{\overrightarrow{r}}_1=300.0\text{m}\widehat{i},$ and hits his second shot 189.0 m with a displacement $\text{Δ}{\overrightarrow{r}}_2=172.0\text{m}\widehat{i}+80.3\text{m}\widehat{j}.$ What is the final displacement of the golf ball from the tee?

A bird flies straight northeast a distance of 95.0 km for 3.0 h. With the x -axis due east and the y -axis due north, what is the displacement in unit vector notation for the bird? What is the average velocity for the trip?

A cyclist rides 5.0 km due east, then 10.0 km $20\text{°}$ west of north. From this point she rides 8.0 km due west. What is the final displacement from where the cyclist started?

New York Rangers defenseman Daniel Girardi stands at the goal and passes a hockey puck 20 m and $45\text{°}$ from straight down the ice to left wing Chris Kreider waiting at the blue line. Kreider waits for Girardi to reach the blue line and passes the puck directly across the ice to him 10 m away. What is the final displacement of the puck? See the following figure.

The position of a particle is $\overrightarrow{r}(t)=4.0t^2\widehat{i}-3.0\widehat{j}+2.0t^3\widehat{k}\text{m}.$ (a) What is the velocity of the particle at 0 s and at $1.0$ s? (b) What is the average velocity between 0 s and $1.0$ s?

Clay Matthews, a linebacker for the Green Bay Packers, can reach a speed of 10.0 m/s. At the start of a play, Matthews runs downfield at $45\text{°}$ with respect to the 50-yard line and covers 8.0 m in 1 s. He then runs straight down the field at $90\text{°}$ with respect to the 50-yard line for 12 m, with an elapsed time of 1.2 s. (a) What is Matthews’ final displacement from the start of the play? (b) What is his average velocity?

The F-35B Lighting II is a short-takeoff and vertical landing fighter jet. If it does a vertical takeoff to 20.00-m height above the ground and then follows a flight path angled at $30\text{°}$ with respect to the ground for 20.00 km, what is the final displacement?