91Ó°ÊÓ

The position of a particle as a function of time is given by CALC$\stackrel{→}{r}=(5\widehat{\text{i}}+4\widehat{\text{j}})t^2\text{m}$, where $t$ is in seconds.

a. What is the particle's distance from the origin at localid="1651417420923" $t=0,2$, and localid="1651417427817" $5\text{s}$
?

b. Find an expression for the particle's velocitylocalid="1651417455538" $\stackrel{→}{v}$as a function of time.

c. What is the particle's speed at localid="1651417472266" $t=0,2$, and localid="1651417482255" $5\text{s}$?

a. What is the angle $\mathrm{ϕ}$between vectors $\stackrel{→}{E}and\stackrel{→}{F}$in FIGURE P3.24?

b. Use geometry and trigonometry to determine the magnitude and direction of $\stackrel{→}{G}=\stackrel{→}{E}+\stackrel{→}{F}.$

c. Use components to determine the magnitude and direction of $\stackrel{→}{G}=\stackrel{→}{E}+\stackrel{→}{F}.$

FIGURE $P3.25$shows vectors $\stackrel{→}{A}\&\stackrel{→}{B}$. Find vector $\stackrel{→}{C}$such that $\stackrel{→}{A}+\stackrel{→}{B}+\stackrel{→}{C}=\stackrel{→}{0}$. Write your answer in component form.

FIGURE $P3.26$shows vectors $\stackrel{→}{A}\&\stackrel{→}{B}$. Find $\stackrel{→}{D}=2\stackrel{→}{A}+\stackrel{→}{B}$. Write your answer in component form.

While vacationing in the mountains you do some hiking. In the morning, your displacement is ${\stackrel{→}{S}}_{\text{morning}}=(2000\text{m}$, east $)+(3000$$\text{m}$, north $)+(200\text{m}$, vertical \()\). After lunch, your displacement is ${\stackrel{→}{S}}_{\text{afternoon}}=(1500\text{m}$, west $)+(2000\text{m}$, north $)−(300\text{m}$, vertical$).$

a. At the end of the hike, how much higher or lower are you compared to your starting point?

b. What is the magnitude of your net displacement for the day?

II The minute hand on a watch is$2.0\text{cm}$in length. What is the displacement vector of the tip of the minute hand

a. From \(8: 00\) to \(8: 20\) A.M.?

b. From \(8: 00\) to \(9: 00\) A.M.?

If $\stackrel{→}{C}=\stackrel{→}{A}+\stackrel{→}{B},$Can $C=0?$Can $C<0?$For each, show how or explain why not.

II You go to an amusement park with your friend Betty, who wants to ride the 30 -m-diameter Ferris wheel. She starts the ride at the lowest point of a wheel that, as you face it, rotates counter clockwise. What is her displacement vector when the wheel has rotated by an angle of ${60}^{°}$? Give your answer as a magnitude and direction.

II Ruth sets out to visit her friend Ward, who lives north and east of her. She starts by driving east, but after she comes to a detour that takes her south before going east again. She then drives east for and runs out of gas, so Ward flies there in his small plane to get her. What is Ward's displacement vector? Give your answer (a) in component form, using a coordinate system in which the -axis points north, and (b) as a magnitude and direction.

I A cannon tilted upward at${30}^{°}$ fires a cannonball with a speed of $100\text{m}/\text{s}$. What is the component of the cannonball's velocity parallel to the ground?