Question

New York is roughly 3000 miles from Seattle. When it is 10:00 A.M. in Seattle, it is 1:00 P.M. in New York. Using this information, estimate (a) the rotational speed of the surface of Earth, (b) the circumference of Earth, and (c) the radius of Earth.

Answer 1

The rotational speed of the Earth is approximately 1000 miles/hour, the circumference is around 24000 miles, and the estimated radius is 3820 miles, based on the data provided about Seattle and New York.

Step-by-step explanation:

The student has asked for an estimation of the Earth's rotational speed, circumference, and radius based on given time-difference and distance details. Using the fact that Seattle and New York are approximately 3000 miles apart and there is a 3-hour time difference we can calculate:

(a) Rotational speed of the surface of Earth

Since the Earth rotates 360 degrees in 24 hours, it rotates 15 degrees per hour (360 degrees / 24 hours). Therefore, since New York and Seattle have 3 hours of time difference, they are 45 degrees apart (15 degrees/hour * 3 hours). To find the rotational speed:

Rotational speed (miles per hour) = Distance / Time = 3000 miles / 3 hours = 1000 miles/hour

(b) Circumference of Earth

To find the circumference, we can extrapolate the distance between the two cities over the entire rotation:

Circumference = Rotational speed per hour * 24 hours = 1000 miles/hour * 24 hours = 24000 miles

(c) Radius of Earth

Using the circumference (C) of the Earth to find the radius (r), we use the formula

C = 2πr

Radius = Circumference / (2π) = 24000 miles / (2 * 3.14159) ≈ 3820 miles

Answer 2

The time difference between New York and Seattle is 3 hours. Since there is a 24 hour time difference in the globe, the equation is expressed (3/24) * circumference of Earth = distance. Distance is equal to 3000 miles hence the circumference is equal to 24,000 miles. The radius then is equal to 24,000/2 pi or 12,000/ pi. The rotational speed is 3000 miles/ 3 hours or 1000 miles/hr.