An astronaut with a mass of $65 \mathrm{~kg}$ is in a rotating space station with a radius of $150 \mathrm{~m}$. She stands on a scale, and the reading is $540 \mathrm{~N}$. (a) At what acceleration do objects fall when dropped near the floor of the space station? (b) Calculate the speed of rotation of the outer rim of the space station. (c) Calculate the period of rotation of the space station.

You are standing $2.7 \mathrm{~m}$ from the centre of a spinning merry-go-round holding one end of a string tied to a $120 \mathrm{~g}$ mass. The merry-go-round has a period of $3.9 \mathrm{~g}$. (a) Draw a system diagram of the situation. (b) Draw an FBD of the mass in Earth's frame of reference. (c) Draw an FBD of the mass in the merry-goround's rotating frame of reference. (d) What angle does the string make with the vertical? (e) Determine the magnitude of the tension in the string.

A river has a steady current of $0.50 \mathrm{~m} / \mathrm{s}$ [E]. A person can swim at $1.2 \mathrm{~m} / \mathrm{s}$ in still water. The person swims upstream $1.0 \mathrm{~km}$ and then back to the starting point. (a) How long does the trip take? (b) Will the time change if he swims downstream $1.0 \mathrm{~km}$ and then back instead? Explain your reasoning. (c) How much time is required to complete the same trip in still water? Why does the trip take longer when there is a current?

An airplane flies $5.0 \times 10^3 \mathrm{~km}$ from Boston to San Francisco at an air speed of $250 \mathrm{~m} / \mathrm{s}$. On the way to San Francisco, the airplane faces a headwind of $50.0 \mathrm{~m} / \mathrm{s}$ blowing from west to east, and a tailwind of the same speed on the way back. (a) Calculate the average speed of the airplane relative to the ground on the way west. (b) Calculate the average speed of the airplane relative to the ground on the way east.

A pilot is required to fly directly from London, United Kingdom, to Rome, Italy, in $3.4 \mathrm{~h}$. The displacement is $1.4 \times 10^3 \mathrm{~km}\left[\mathrm{~S} 43^{\circ} \mathrm{E}\right.$ ]. The wind velocity reported from the ground is $55 \mathrm{~km} / \mathrm{h}$ [S]. Determine the required velocity of the plane relative to the air.

A helicopter travels at a velocity of $62 \mathrm{~m} / \mathrm{s}$ [N] with respect to the air. Calculate the velocity of the helicopter with respect to Earth when the wind velocity is as follows: (a) $18 \mathrm{~m} / \mathrm{s}[\mathrm{N}]$ (b) $18 \mathrm{~m} / \mathrm{s}$ [S] (c) $18 \mathrm{~m} / \mathrm{s}[\mathrm{W}]$ (d) $18 \mathrm{~m} / \mathrm{s}\left[\mathrm{N} 42^{\circ} \mathrm{W}\right]$

A football is thrown from the edge of a cliff from a height of $22 \mathrm{~m}$ at a velocity of $18 \mathrm{~m} / \mathrm{s}\left[39^{\circ}\right.$ above the horizontal]. A player at the bottom of the cliff is $12 \mathrm{~m}$ away from the base of the cliff and runs at a maximum speed of $6.0 \mathrm{~m} / \mathrm{s}$ to catch the ball. Is it possible for the player to catch the ball? Support your answer with calculations.

mass 1 does not slide with respect to the surface when the horizontal force shown is applied. Determine the magnitude of the horizontal force in figure mentioned. Assume there is no friction.

A car moves in a horizontal circle on a test track with a radius of $1.2 \times 10^2 \mathrm{~m}$. The coefficient of static friction between the tires and the road is 0.72. Draw an FBD, and calculate the maximum speed of the car.

Consider a banked curve on an exit ramp for a highway in the middle of winter when the road surface is covered with very slippery ice. (a) How does the banking angle of the road help drivers make it safely around the curve? What force (or component of force) is responsible? Explain your reasoning. (b) Explain why drivers must go much more slowly under these circumstances. (c) A student claims, "If banking angles help drivers safely navigate curved sections of road, why not make the banking angles significantly larger?" Identify one problem that might occur if this suggestion were used. Justify your answer.

Consider an airplane that travels at $800.0 \mathrm{~km} / \mathrm{h}[\mathrm{E}]$ against a wind with a velocity of $75.0 \mathrm{~km} / \mathrm{h}\left[\mathrm{W} 30.0^{\circ} \mathrm{S}\right]$. (a) Determine the speed of the plane with respect to the ground. (b) Calculate how many kilometres south of its due east course the plane would be displaced after $3.0 \mathrm{~h}$ of flight.

For the same bluff as in Question 77, make the following assumptions: the terrain south and southeast of the Cap aux Diamants has the same level as the river, the initial speed of the projectile is $290 \mathrm{~m} / \mathrm{s}$, and the projectile launcher points up at an angle of $24^{\circ}$ above the horizontal. (a) Calculate the time of flight for the projectile. (b) Calculate the range of the projectile, in kilometres. (c) What would the range be if you set the angle of the projectile launcher at $45^{\circ}$ above the horizontal? (d) Consider the range equation when the net vertical displacement is zero. Explain why your answer to $(\mathrm{c})$ equals the greatest possible range for the given initial speed of the projectile.

Using an online resource, design your own roller coaster. List each design feature you have included and explain your reasoning. Explain how you have kept the ride exciting while keeping it safe for customers. Decide on a theme for your roller coaster, and try to include the theme in your design.

Research windmills and wind turbines, how they work, and their effect on the environment. (a) How do windmills and wind turbines use the principles of dynamics and circular motion to generate power? Include a simple diagram in your answer. (b) What is the environmental impact of wind power and wind farms?