Suppose a driver's car needs to travel 46.4 miles in 1.000 hour at a constant speed. If the tires of the car have a rolling radius of 28.4 cm, what will be the period of rotation of each tire?

Suppose a moon of a planet in a distant solar system has an average orbital radius of 2.62 x 108 m. If it completes its orbit in 20.1 earth days, what is the average gravitational acceleration keeping it in orbit around the planet?

Vc = 46.4mi/3600s * 1600m/mi = 20.62 m/s

Circumference=pi*2r=3.14 * 0.568=1.784 m

Period =(1.784m/20.62m)*1s. = 0.0865 s.

To find the period of rotation for each tire, we can use the formula:

Period of rotation = Distance traveled / Circumference of the tire

1. First, let's convert the rolling radius of the tire from centimeters to miles. Since there are 1609.34 meters in a mile, we need to convert centimeters to meters and then meters to miles:

Rolling radius in meters = 28.4 cm * 0.01 m/cm = 0.284 m
Rolling radius in miles = 0.284 m / 1609.34 m/mile = 0.000176693 miles

2. Next, let's calculate the circumference of the tire using the rolling radius:

Circumference of the tire = 2 * π * rolling radius
Circumference of the tire = 2 * 3.14159 * 0.000176693 miles = 0.00111052 miles

3. Finally, calculate the period of rotation:

Period of rotation = Distance traveled / Circumference of the tire
Period of rotation = 46.4 miles / 0.00111052 miles = 41789.4968 rotations

So, the period of rotation for each tire will be approximately 41789.4968 rotations.

For the second question regarding the average gravitational acceleration, we can use the formula:

Gravitational acceleration = (2 * π * Average orbital radius) / Period of orbit^2

1. The average orbital radius of the moon is given as 2.62 x 10^8 m.

2. The period of orbit is given as 20.1 earth days. We need to convert it to seconds since acceleration is measured in meters per second squared. There are 24 hours in a day and 60 minutes in an hour, so:

Period of orbit in seconds = 20.1 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute

3. Finally, calculate the average gravitational acceleration:

Gravitational acceleration = (2 * π * Average orbital radius) / Period of orbit^2
Gravitational acceleration = (2 * 3.14159 * 2.62 x 10^8 m) / (20.1 days * 24 hours/day * 60 minutes/hour * 60 seconds/minute)^2

Calculate the value and you'll have the average gravitational acceleration keeping the moon in orbit around the planet.