A satellite is in an elliptic orbit around the Earth (Fig. 8-51). Its speed at the perigee A is $8650\mathrm{~m/s}$. $(a)$ Use conservation of energy to determine its speed at B.

(II) Take into account the Earth's rotational speed ($1\ \text{rev/day}$) and determine the necessary "escape velocity," with respect to the Earth, for a rocket to escape if fired from the Earth at the equator in a direction (a) eastward

Proper design of automobile braking systems must account for heat buildup under heavy braking. Calculate the thermal energy dissipated from brakes in a $1500\mathrm{-kg}$ car that descends a $17^\circ$ hill. The car begins braking when its speed is $95\ \text{km/h}$ and slows to a speed of $35\ \text{km/h}$ in a distance of $0.30\ \text{km}$ measured along the road

(III) The comet Hale-Bopp has an orbital period of $2400\:\text{years}$. (c ) What is the ratio of the speed at the closest point to the speed at the farthest point?

The Sun revolves around the center of our Milky Way Galaxy (Fig. $6-39$) at a distance of about $30,000$ light-years from the center ($1$ ly=$9.5\times 10^{15}$m). If it takes about $200$ million years to make one revolution, estimate the mass of our Galaxy. Assume that the mass distribution of our Galaxy is concentrated mostly in a central uniform sphere. If all the stars had about the mass of our Sun ($2\times10^{30}$kg), how many stars would there be in our Galaxy?

A mass m is gently placed on the end of a freely hanging spring. The mass then falls 33 cm before it stops and begins to rise. What is the frequency of the oscillation?

The comet Hale-Bopp has an orbital period of $2400$ years. What is its mean distance from the Sun?

The Milky Way galaxy rotates about its center with a period of about 200 million yr. The Sun is

$$2 \times 10 ^ { 20 }$$

m from the center of the galaxy. How fast is the Sun moving with respect to the center of the galaxy?

The comet Hale-Bopp has an orbital period of $2400$ years. At its closest approach, the comet is about $1.0 \mathrm{AU}$ from the Sun ( $1 \mathrm{AU}=$ distance from Earth to the Sun). What is the farthest distance?

A $56\mathrm{-kg}$ student runs at $6.0\mathrm{~m/s}$, grabs a hanging $10.0\text{-m-long}$ rope, and swings out over a lake (Fig. 8-49). He releases the rope when his velocity is zero. $(c)$ What is the maximum tension in the rope during the swing?

A $56\mathrm{-kg}$ student runs at $6.0\mathrm{~m/s}$, grabs a hanging $10.0\text{-m-long}$ rope, and swings out over a lake (Fig. 8-49). He releases the rope when his velocity is zero. $(a)$ What is the angle $\theta$ when he releases the rope?

(II) Two Earth satellites, A and B, each of mass $m = 950\ \text{kg}$, are launched into circular orbits around the Earth's center. Satellite A orbits at an altitude of $12,600\ \text{kg}$. (b) What are the kinetic energies of the two satellites?

Two equal-mass stars maintain a constant distance apart of $8.0 \times 10^{11} \mathrm{~m}$ and rotate about a point midway between them at a rate of one revolution every $12.6$ yr. What must be the mass of each star?

A $56\mathrm{-kg}$ student runs at $6.0\mathrm{~m/s}$, grabs a hanging $10.0\text{-m-long}$ rope, and swings out over a lake (Fig. 8-49). He releases the rope when his velocity is zero. $(b)$ What is the tension in the rope just before he releases it?