A student throws a ball vertically upward. It takes the ball $0.50 \mathrm{~s}$ to come to a stop and another $0.50 \mathrm{~s}$ to return to the student. The maximum height of the ball is $1.225 \mathrm{~m}$. Calculate the initial speed with which the student threw the ball.

Gas centrifuge technology is an emerging technology. The technology enriches mined uranium to levels at which it can be used to generate nuclear power. The use of centrifuges increases the concentration of the isotope uranium-235 in the uranium. Research the various applications of gas centrifuge technology. How has it affected the efficiency of energy production?

A parachutist falling at a terminal velocity of $50.0 \mathrm{~m} / \mathrm{s}$ [down] opens her parachute. At that point a net acceleration of about $12.5 \mathrm{~m} / \mathrm{s}^2$ [up] reduces her velocity to about $10.0 \mathrm{~m} / \mathrm{s}$ [down]. Calculate the time over which this acceleration takes place.

Research the effects of uniform circular motion on growing plants. What effects would a continuously spinning pot of soil have on the grass seed planted in it? How would the grass grow differently?

A snowmobile is originally at the point with position vector $29.0 \mathrm{~m}$ at $95.0^{\circ}$ counterclockwise from the $x$ axis, moving with velocity $4.50 \mathrm{~m} / \mathrm{s}$ at $40.0^{\circ}$. It moves with constant acceleration $1.90 \mathrm{~m} / \mathrm{s}^2$ at $200^{\circ}$. After $5.00 \mathrm{~s}$ have elapsed, find
(b) its position vector.

A snowmobile is originally at the point with position vector 29.0 m at $95.0^{\circ}$ counterclockwise from the x axis, moving with velocity $4.50 \mathrm{m} / \mathrm{s}$ at $40.0^{\circ} .$ It moves with constant acceleration $1.90 \mathrm{m} / \mathrm{s}^{2}$ at $200^{\circ} .$ After 5.00 s have elapsed, find (a) its velocity and (b) its position vector.

A home run is hit in such a way that the baseball just clears a wall 21 m high, located 130 m from home plate. The ball is hit at an angle of $35 ^ { \circ }$ to the horizontal, and air resistance is negligible. Find the velocity components and the speed of the ball when it reaches the wall. (Assume the ball is hit at a height of 1.0 m above the ground.)

A sprinter accelerates at a constant rate of $4.8 \mathrm{~m} / \mathrm{s}^2$ during the first $10.0 \mathrm{~m}$ of a $100.0 \mathrm{~m}$ event. Determine the runner's speed at the end of the first $10.0 \mathrm{~m}$ of the race.

Research the effects of the Coriolis force in meteorology. In your own words, describe the effect using the movement of a hurricane as an example.

A fish swimming in a horizontal plane has velocity $\mathbf{v}_i=(4.00 \hat{\mathbf{i}}+1.00 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}$ at a point in the ocean where the position relative to a certain rock is $\mathbf{r}_i=(10.0 \hat{\mathbf{i}}-4.00 \hat{\mathbf{j}}) \mathrm{m}$. After the fish swims with constant acceleration for $20.0 \mathrm{~s}$, its velocity is $\mathbf{v}=(20.0 \hat{\mathbf{i}}-5.00 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}$. If the fish maintains constant acceleration, where is it at $t=25.0 \mathrm{~s}$, and in what direction is it moving?

A fish swimming in a horizontal plane has velocity $\mathbf{v}_i=(4.00 \hat{\mathbf{i}}+1.00 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}$ at a point in the ocean where the position relative to a certain rock is $\mathbf{r}_i=(10.0 \hat{\mathbf{i}}-4.00 \hat{\mathbf{j}}) \mathrm{m}$. After the fish swims with constant acceleration for $20.0 \mathrm{~s}$, its velocity is $\mathbf{v}=(20.0 \hat{\mathbf{i}}-5.00 \hat{\mathbf{j}}) \mathrm{m} / \mathrm{s}$. What is the direction of the acceleration with respect to unit vector $\hat{i}$ ?

A fish swimming in a horizontal plane has velocity m/s at a point in the ocean where the position relative to a certain rock is m. After the fish swims with constant acceleration for 20.0 s, its velocity is m/s. (a) What are the components of the acceleration of the fish? (b) What is the direction of its acceleration with respect to unit vector ? (c) If the fish maintains constant acceleration, where is it at t = 25.0 s and in what direction is it moving? $\overrightarrow { \mathbf { v } } _ { i } = ( 4.00 \hat { \mathbf { i } } + 1.00 \hat { \mathbf { j } } )$ $\vec { r } _ { i } = ( 10.0 \hat { \mathrm { i } } - 4.00 \hat { \mathrm { j } } )$ $\overrightarrow { \mathbf { v } } = ( 20.0 \hat { \mathbf { i } } - 5.00 \hat { \mathbf { j } } )$ $\hat{i}$

Research the history of roller coasters, showing how the designs have changed over the centuries. Present your findings in a timeline, on paper, as a Wiki page, as an electronic slide presentation, or in another format of your choosing.

Suppose the position vector for a particle is given as a function of time by , with x(t ) = at + b and y(t ) = ct2 + d, where a 5 =.00 m/s, b = 1.00 m, c = 0.125 m/s2, and d = 1.00 m. (a) Calculate the average velocity during the time interval from t = 2.00 s to t = 4.00 s. (b) Determine the velocity and the speed at t = 2.00 s. $\overrightarrow { \mathbf { r } } ( t ) = x ( t ) \hat { \mathbf { i } } + y ( t ) \hat { \mathbf { j } }$