91Ó°ÊÓ

Answer Problems 3 through 5 by choosing one of the eight labeled acceleration vectors or selecting option $\text{I}:\stackrel{→}{a}=\stackrel{→}{0}$

4. At this instant, the particle is speeding up and curving upward. What is the direction of its acceleration?

A projectile is launched at an angle of ${30}^{°}$.

a. Is there any point on the trajectory where$\stackrel{→}{v}$and$\stackrel{→}{a}$are parallel to each other? If so, where?

b. Is there any point where$\stackrel{→}{v}$and$\stackrel{→}{a}$are perpendicular to each

other? It so, where?

A 5.0-m-diameter merry-go-round is initially turning with a $4.0\text{s}$period. It slows down and stops in $20\text{s}$.

a. Before slowing, what is the speed of a child on the rim?

b. How many revolutions does the merry-go-round make as it stops?

II An electric fan goes from rest to$1800\text{rpm}$ in $4.0\text{s}$. What is its angular acceleration?

A bicycle wheel is rotating at $50\text{rpm}$, and when the cyclist begins to pedal harder, giving the wheel a constant angular acceleration of $0.50\text{rad}/{\text{s}}^2$.

a. What is the wheel's angular velocity, in rpm, $10\text{s}$later?

b. How many revolutions does the wheel make during this time?

Starting from rest, a DVD steadily accelerates to $500\text{rpm}$in $1.0\text{s}$, rotates at this angular speed for $3.0\text{s}$, then steadily decelerates to a halt in $2.0\text{s}$. How many revolutions does it make?

A spaceship maneuvering near Planet Zeta is located at$\widehat{r}=(600\widehat{i}−400\widehat{j}+200\widehat{k})×{10}^3\text{km}$ , relative to the planet, and traveling at $\stackrel{→}{v}=9500\widehat{\mathrm{Ä\pm }}\text{m}/\text{s}$. It turns on its thruster engine and accelerates with $\stackrel{→}{a}=(40\widehat{\mathrm{Ä\pm }}−20\widehat{k})\text{m}/{\text{s}}^2$for $35\text{min}$. What is the spaceship's position when the engine shuts off? Give your answer as a position vector measured in $\text{km}$.

A particle moving in the xy--plane has velocity ${\stackrel{→}{v}}_0=v_{0x}\widehat{\mathrm{Ä\pm }}+v_{0y}\widehat{J}$CALC at$t=0$ . It undergoes acceleration , where $b$and $c$are constants. Find an expression for the particle's velocity at a later time $t$.

A projectile’s horizontal range over level ground is $\raisebox{1ex}{${v_0}^2\sin 2\mathrm{θ}$}\!\left/ \!\raisebox{-1ex}{$g$}\right.$. At what launch angle or angles will the projectile land at half of its maximum possible range?

a. A projectile is launched with speed $v_0$and angle $\mathrm{θ}$. Derive an

expression for the projectile’s maximum height $h$.

b. A baseball is hit with a speed of 33.6 m/s. Calculate its

height and the distance traveled if it is hit at angles of

30.0°, 45.0°, and 60.0°.