I am so confused
How fast (in km/hr) must a plane fly along the Earth's equator so that the Sun stands still relative to the passengers. The radius of the Earth is 6400 km
Nevermind, I'm dumb. Got it.
Flying relative to what? Earth's surface?
To understand this problem, we can start by considering the rotation of the Earth. The Earth rotates once every 24 hours, which means that a point on the equator travels a distance equal to the Earth's circumference (given by 2π times the radius) in that time.
The circumference of the Earth can be calculated as:
C = 2π * r
where r is the radius of the Earth (given as 6400 km).
Since the Sun appears to stand still relative to the passengers, we can conclude that the plane needs to travel the same distance as the Earth's circumference in 24 hours. This is because the apparent motion of the Sun is caused by the rotation of the Earth.
So, the plane should be able to cover the circumference of the Earth in 24 hours, or a distance of C. To calculate the speed at which the plane needs to fly, we divide the distance traveled by the time taken:
Speed = Distance / Time
In this case, the distance traveled is the circumference of the Earth, C, and the time taken is 24 hours (or 24 hours converted to seconds, if needed). Let's calculate the speed:
Speed = C / (24 hours)
To convert hours to seconds, we know that 1 hour is equal to 3600 seconds, so:
Speed = C / (24 hours * 3600 seconds per hour)
Plugging in the value for C, the circumference of the Earth:
Speed = (2π * r) / (24 hours * 3600 seconds per hour)
Substituting the given radius of the Earth, r = 6400 km:
Speed = (2π * 6400 km) / (24 hours * 3600 seconds per hour)
Now, we can calculate the speed in kilometers per hour by converting the distance traveled (2π * 6400 km) from kilometers per second to kilometers per hour:
Speed = (2π * 6400 km) / (24 hours * 3600 seconds per hour) * 3600 seconds per hour
Evaluating this expression will give us the required speed in kilometers per hour.