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A satellite is rotating around Earth at 0.25 radian per hour at an altitude of 242 km above Earth. If the radius of Earth is 6378 kilometers, find the linear speed of the satellite in kilometers per hour.

1655 kilometers per hour

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Key equations

arc length s = r θ
area of a sector A = 1 2 θ r 2
angular speed ω = θ t
linear speed v = s t
linear speed related to angular speed v = r ω

Key concepts

  • An angle is formed from the union of two rays, by keeping the initial side fixed and rotating the terminal side. The amount of rotation determines the measure of the angle.
  • An angle is in standard position if its vertex is at the origin and its initial side lies along the positive x -axis. A positive angle is measured counterclockwise from the initial side and a negative angle is measured clockwise.
  • To draw an angle in standard position, draw the initial side along the positive x -axis and then place the terminal side according to the fraction of a full rotation the angle represents. See [link] .
  • In addition to degrees, the measure of an angle can be described in radians. See [link] .
  • To convert between degrees and radians, use the proportion θ 180 = θ R π . See [link] and [link] .
  • Two angles that have the same terminal side are called coterminal angles.
  • We can find coterminal angles by adding or subtracting 360° or 2 π . See [link] and [link] .
  • Coterminal angles can be found using radians just as they are for degrees. See [link] .
  • The length of a circular arc is a fraction of the circumference of the entire circle. See [link] .
  • The area of sector is a fraction of the area of the entire circle. See [link] .
  • An object moving in a circular path has both linear and angular speed.
  • The angular speed of an object traveling in a circular path is the measure of the angle through which it turns in a unit of time. See [link] .
  • The linear speed of an object traveling along a circular path is the distance it travels in a unit of time. See [link] .

Section exercises

Verbal

Draw an angle in standard position. Label the vertex, initial side, and terminal side.


Graph of a circle with an angle inscribed, showing the initial side, terminal side, and vertex.

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Explain why there are an infinite number of angles that are coterminal to a certain angle.

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State what a positive or negative angle signifies, and explain how to draw each.

Whether the angle is positive or negative determines the direction. A positive angle is drawn in the counterclockwise direction, and a negative angle is drawn in the clockwise direction.

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How does radian measure of an angle compare to the degree measure? Include an explanation of 1 radian in your paragraph.

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Explain the differences between linear speed and angular speed when describing motion along a circular path.

Linear speed is a measurement found by calculating distance of an arc compared to time. Angular speed is a measurement found by calculating the angle of an arc compared to time.

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Questions & Answers

I don't understand how radicals works pls
Kenny Reply
How look for the general solution of a trig function
collins Reply
stock therom F=(x2+y2) i-2xy J jaha x=a y=o y=b
Saurabh Reply
root under 3-root under 2 by 5 y square
Himanshu Reply
The sum of the first n terms of a certain series is 2^n-1, Show that , this series is Geometric and Find the formula of the n^th
amani Reply
cosA\1+sinA=secA-tanA
Aasik Reply
why two x + seven is equal to nineteen.
Kingsley Reply
The numbers cannot be combined with the x
Othman
2x + 7 =19
humberto
2x +7=19. 2x=19 - 7 2x=12 x=6
Yvonne
because x is 6
SAIDI
what is the best practice that will address the issue on this topic? anyone who can help me. i'm working on my action research.
Melanie Reply
simplify each radical by removing as many factors as possible (a) √75
Jason Reply
how is infinity bidder from undefined?
Karl Reply
what is the value of x in 4x-2+3
Vishal Reply
give the complete question
Shanky
4x=3-2 4x=1 x=1+4 x=5 5x
Olaiya
hi can you give another equation I'd like to solve it
Daniel
what is the value of x in 4x-2+3
Olaiya
if 4x-2+3 = 0 then 4x = 2-3 4x = -1 x = -(1÷4) is the answer.
Jacob
4x-2+3 4x=-3+2 4×=-1 4×/4=-1/4
LUTHO
then x=-1/4
LUTHO
4x-2+3 4x=-3+2 4x=-1 4x÷4=-1÷4 x=-1÷4
LUTHO
A research student is working with a culture of bacteria that doubles in size every twenty minutes. The initial population count was  1350  bacteria. Rounding to five significant digits, write an exponential equation representing this situation. To the nearest whole number, what is the population size after  3  hours?
David Reply
v=lbh calculate the volume if i.l=5cm, b=2cm ,h=3cm
Haidar Reply
Need help with math
Peya
can you help me on this topic of Geometry if l help you
litshani
( cosec Q _ cot Q ) whole spuare = 1_cosQ / 1+cosQ
Aarav Reply
A guy wire for a suspension bridge runs from the ground diagonally to the top of the closest pylon to make a triangle. We can use the Pythagorean Theorem to find the length of guy wire needed. The square of the distance between the wire on the ground and the pylon on the ground is 90,000 feet. The square of the height of the pylon is 160,000 feet. So, the length of the guy wire can be found by evaluating √(90000+160000). What is the length of the guy wire?
Maxwell Reply

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Source:  OpenStax, Algebra and trigonometry. OpenStax CNX. Nov 14, 2016 Download for free at https://legacy.cnx.org/content/col11758/1.6
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