assuming that Earth's radius is 6400 km, find the linear velocity of Quito, Equador, a city on the equator. (Use pi=3.1416 and 1.6 km=1 mile).
I guess we are to do miles per hour ?
v = omega * r
omega = 2 pi /24 hr
r = 6.4*10^3 km (1 mile/1.6 km) = 4,000 miles
so
v = 4000 miles (2 pi/ 24 hr)
=3333 miles/ hour
(2 pi * 6400 km)/(24 hours)
That will give you the answer in km/h. Divide by 1.6 for miles per hour.
Actually, a better conversion factor with five significant figures is 1.6093 km/mile
It makes no sense to have five significant figures for pi and only two for the km-to-miles factor
my choices are
2094.4 mph
209.4 mph
1047.2 mph
104.7 mph
LOL - the textbook writer is using a calculator with pi on it but not the unit conversions :)
v = 4000 miles (2 pi/ 24 hr)
=1047.2 miles/ hour
thnks
To find the linear velocity of Quito, Ecuador, we need to use the formula:
Linear velocity = distance / time
In this case, the distance is the circumference of the Earth at the equator, and the time is the time it takes for one complete rotation, which is 24 hours.
First, let's find the circumference of the Earth at the equator using the given radius of 6400 km. The circumference is calculated using the formula:
Circumference = 2 * pi * radius
Substituting the given values:
Circumference = 2 * 3.1416 * 6400 km
Now, we need to convert kilometers to miles using the conversion factor 1.6 km = 1 mile:
Circumference = 2 * 3.1416 * 6400 km / 1.6 km/mile
Simplifying the above equation, we get:
Circumference = 2 * 3.1416 * 6400 / 1.6 miles
To find the linear velocity, we need to divide the circumference by the time it takes for one complete rotation, which is 24 hours:
Linear velocity = Circumference / Time
Substituting the values:
Linear velocity = (2 * 3.1416 * 6400 miles) / 24 hours
Simplifying the above equation, we get:
Linear velocity = (3.1416 * 6400 / 12) miles/hour
Calculating this expression gives us the linear velocity of Quito, Ecuador.