Chapter 4: Kinematics in Two Dimensions

II As the earth rotates, what is the speed of (a) a physics student in Miami, Florida, at latitude ${26}^{°}$, and (b) a physics student in Fairbanks, Alaska, at latitude ${65}^{°}$? Ignore the revolution of the earth around the sun. The radius of the earth is $6400\text{km}$.

I How fast must a plane fly along the earth's equator so that the sun stands still relative to the passengers? In which direction must the plane fly, east to west or west to east? Give your answer in both $\text{km}/\text{h}$and $\text{mph}$. The earth's radius is $6400\text{km}$.

Answer Problems 3 through 5 by choosing one of the eight labeled acceleration vectors or selecting option

3. At this instant, the particle has steady speed and is curving to the right. What is the direction of its acceleration?

Tarzan swings through the jungle by hanging from a vine.

a. Immediately after stepping off a branch to swing over to another tree, is Tarzan's acceleration$\overrightarrow{a}$zero or not zero? If not zero, which way does it point? Explain.

b. Answer the same question at the lowest point in Tarzan's swing.

II A 3000 -m-high mountain is located on the equator. How much faster does a climber on top of the mountain move than a surfer at a nearby beach? The earth's radius is $6400\text{km}$.

Peregrine falcons are known for their manoeuvring ability. In a BI0 tight circular turn, a falcon can attain a centripetal acceleration 1.5 times the free-fall acceleration. What is the radius of the turn if the falcon is flying at $25\text{m}/\text{s}$?

I To withstand "g-forces" of up to$10\text{g}$ 's, caused by suddenly BI0 pulling out of a steep dive, fighter jet pilots train on a "human centrifuge." $10\text{g}$'s is an acceleration of $98\text{m}/{\text{s}}^2$. If the length of the centrifuge arm is $12\text{m}$, at what speed is the rider moving when she experiences 10 g's?

The radius of the earth's very nearly circular orbit around the sun is $1.5\times {10}^{11}\text{m}$. Find the magnitude of the earth's (a) velocity, (b) angular velocity, and (c) centripetal acceleration as it travels around the sun. Assume a year of 365 days.

34. II A speck of dust on a spinning DVD has a centripetal acceleration of $20\text{m}/{\text{s}}^2$.

a. What is the acceleration of a different speck of dust that is twice as far from the center of the disk?

b. What would be the acceleration of the first speck of dust if the disk's angular velocity was doubled?

35. II Your roommate is working on his bicycle and has the bike upside down. He spins the 60-cm-diameter wheel, and you notice that a pebble stuck in the tread goes by three times every second. What are the pebble's speed and acceleration?