A ball is to be shot from the level ground toward a wall at distance $x$ (shown in the figure). The figure shows the $y$ component $v_{\mathrm{y}}$ of the ball's velocity just as it would reach the wall, as a function of that distance $x$. The scaling is set by $v_{\mathrm{ys}}=5.0 \mathrm{m} {\mathrm{s}}^{-1}$ and $x_{\mathrm{s}}=20 \mathrm{m}$. What is the launch angle?

   

            $\left(a\right)$                                                                             $\left(b\right)$

A baseball is hit at a height $h=1.00 \mathrm{m}$ and then caught at the same height. It travels alongside a wall, moving up past the top of the wall $1.00 \mathrm{s}$ after it is hit and then down past the top of the wall $4.00 \mathrm{s}$ later, at distance $D=50.0 \mathrm{m}$ farther along the wall. $\left(a\right)$ What horizontal distance is traveled by the ball from hit to catch? What are the $\left(b\right)$ magnitude and $\left(c\right)$ angle (relative to the horizontal) of the ball's velocity just after being hit? $\left(d\right)$ How high is the wall?

A ball is to be shot from ground level with a certain speed showing the range $R$ versus the launch angle ${\mathrm{\theta }}_0$. The value of ${\mathrm{\theta }}_0$ determines the fight time. Let $t_{\max }$ represent the maximum flight time. What is the least speed the ball will have during its flight if ${\mathrm{\theta }}_0$ is chosen such that the flight time is $0.500t_{\max }$?

An earth satellite moves in a circular orbit $750 \mathrm{km}$ above the earth's surface with a period of $98.0 \min$. What are the $\left(a\right)$ speed and $\left(b\right)$ magnitude of the centripetal acceleration of the satellite?

A carnival merry-go-round rotates about a vertical axis at a constant rate. A man standing on the edge has a constant speed of $3.66 \mathrm{m} {\mathrm{s}}^{-1}$ and a centripetal acceleration $\overrightarrow{a}$ of magnitude $1.83 \mathrm{m} {\mathrm{s}}^{-2}$. The position vector $\overrightarrow{r}$ locates him relative to the rotation axis. $\left(a\right)$ What is the magnitude of $\overrightarrow{r}$? What is the direction of when $\overrightarrow{a}$ is directed $\left(b\right)$ due east and $\left(c\right)$ due south?

A rotating fan completes $1100 \mathrm{revolutions} \mathrm{per} \mathrm{minute}$. Consider the tip of a blade, at a radius of $0.15 \mathrm{m}$. $\left(a\right)$ Through what distance does the tip move in one revolution? What are $\left(b\right)$ the tip's speed and $\left(c\right)$ the magnitude of its acceleration? $\left(d\right)$ what is the period of the motion?

A centripetal-acceleration addict rides in uniform circular motion with period $T=2.0 \mathrm{s}$ and radius $r=3.50 \mathrm{m}$. At $t_1$ his acceleration is $\overrightarrow{a}=\left(6.00 \mathrm{m} {\mathrm{s}}^{-2}\right)\hat{\mathrm{i}}+\left(-4.00 \mathrm{m} {\mathrm{s}}^{-2}\right)\hat{\mathrm{j}}$. At that instant, what are the values of $\left(a\right)$ $\overrightarrow{v}·\overrightarrow{a}$ and $\left(b\right)$ $\overrightarrow{r}\times \overrightarrow{a}$?