Respuesta :
Answer:
A)
62/3 = 20.67 hours
B)
60 hours
C)
2074.29 miles
Step-by-step explanation:
If we assume the earth is a perfect circle, then in a complete rotation the earth covers 360 degrees or 2π radians.
A)
In 24 hours the earth rotates through an angle of 360 degrees. We are required to determine the duration it takes to rotate through 310 degrees. Let x be the duration it takes the earth to rotate through 310 degrees, then the following proportions hold;
(24/360) = (x/310)
solving for x;
x = (24/360) * 310 = 62/3 = 20.67 hours
B)
In 24 hours the earth rotates through an angle of 2π radians. We are required to determine the duration it takes to rotate through 5π radians. Let x be the duration it takes the earth to rotate through 5π radians, then the following proportions hold;
(24/2π radians) = (x/5π radians)
Solving for x;
x = (24/2π radians)*5π radians = 60 hours
C)
If the diameter of the earth is 7920 miles, then in 24 hours a point on the equator will rotate through a distance equal to the circumference of the Earth. Using the formula for the circumference of a circle we have;
circumference = 2*π*R = π*D
= 7920π miles
Therefore, the speed of the earth is approximately;
(7920π miles)/(24 hours) = 330π miles/hr
The distance covered by a point in 2 hours will thus be;
330π * 2 = 660π miles = 2074.29 miles
Answer:
Part A). In 20 hr 24 minutes earth rotate 310°.
Part B). In 19 hr 6 minutes earth rotate 5 radians
Part C). 2072.4 miles point on equator rotates in 2 hours.
Step-by-step explanation:
Degree that earth rotate in 24 hour = 360°
Number of radian that earth rotate in 24 hour = 2π radian
Part A).
Time taken to rotate 360° = 24 hours
Time taken to rotate 1° = [tex]\frac{24}{360}=\frac{1}{15}\,hours[/tex]
Time taken to rotate 310° = [tex]310\times\frac{1}{15}=20\frac{2}{5}=20\,hr\:24\,minutes[/tex]
Part B).
Time taken to rotate 2π radian = 24 hours
Time taken to rotate 1 radian = [tex]\frac{24}{2\pi}=\frac{12}{\pi}\,hours[/tex]
Time taken to rotate 5 radian = [tex]5\times\frac{12}{\pi}=\frac{60}{\pi}=19.1\.hr=19\,hr\:6\,minutes[/tex]
Part C).
Diameter of Earth = 7920 miles
Radius of earth, r = 3960 miles
Degree of rotation in 1 hours = [tex]\frac{360}{24}=15^{\circ}[/tex]
Degree of rotation in 2 hours , [tex\theta[/tex] = 15 × 2 = 30°
Length of the arc for angle 30° of circle with radius 3960 miles = Distance covered by point in 2 hours.
Length of the arc = [tex]\frac{\theta}{360^{\circ}}\times2\pi r=\frac{30}{360}\times2\times3.14\times3960=2072.4\:miles[/tex]
Therefore, Part A). In 20 hr 24 minutes earth rotate 310°.
Part B). In 19 hr 6 minutes earth rotate 5 radians
Part C). 2072.4 miles point on equator rotates in 2 hours.
