Question

(12) The Earth is one astronomical unit from the
sun i.e. 1 AU= 93 million miles. The angular speed of the Earth
eling around the sun is approximately 0.9863 degrees per
day. If we assume the orbit of the Earth is completely circular,
what is the linear speed in miles per hour?
-- miles per hour
If it takes you 4 hours to drive to Dallas for OU-Texas week-
end, how much of a revolution did the Earth make in that time?
Round to FOUR decimal places ( in revolutions)

Answer 1

Answer:

3,821,912.5 miles/hour is the linear speed of the earth around the sun.

The Earth make 0.02616 revolutions in 4 hours.

Step-by-step explanation:

$v = r\times \omega$

v =  linear speed

r = radius from the center

$\omega$= angular speed

The angular speed of the Earth around the sun = 0.9863 degrees/day

Distance of the earth from the sun = r = 1 AU = $93\times 10^{6} miles$

Linear speed of earth around the sun = v

v = $93\times 10^{6} miles\times 0.9863 degrees/day=91,725,900 miles/day$

1 day = 24 hours

v=$\frac{91,725,900 miles}{24 hours}=3,821,912.5 miles/hour$

3,821,912.5 miles/hour is the linear speed of the earth around the sun.

Duration  of drive from Dallas to Texas = 4 hours

Miles of revolution of earth covered in 4 hours :

$3,821,912.5 miles/hour\times 4 hr = 15,287,650 miles$

$1 revolution = 2\pi r$

$1 revolution = 2\times 3.14\times 93\times 10^6 miles$

The revolution of earth in 15,287,650 miles will be:

$\frac{1}{2\times 3.14\times 93\times 10^6 miles}\times 15,287,650$

=0.026162420 revolution ≈ 0.02616 revolutions

The Earth make 0.02616 revolutions in 4 hours.