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An orange is rolled on the floor in a straight line from one person to another person. The orange has a radius of 4 cm and there is a fixed point P located on theorange. Let the person rolling the orange represent the origin. Find parametric equations in terms of describing the cycloid traced out by P.AnswerKeypadKeyboard Shortcuts

An Orange Is Rolled On The Floor In A Straight Line From One Person To Another Person The Orange Has A Radius Of 4 Cm And There Is A Fixed Point P Located On Th class=

Sagot :

Answer:

Given that,

An orange is rolled on the floor in a straight line from one person to another person

The orange has a radius of 4 cm and there is a fixed point P located on the orange.

To find the The orange has a radius of 4 cm and there is a fixed point P located on the

orange.

Explanation:

A cycloid is a curve that rolls along a particular line, leaving traces behind, which look like a few half circles with specific radii R.

Cycloid is an even linear and circular motion with a constant speed.

The parametric equation will bw,

[tex]\begin{gathered} x=r\left(θ−sinθ\right) \\ y=r\left(1−cosθ\right) \end{gathered}[/tex]

where r – radius of the circle, θ – an angle at which the circle is moving.

Here, we get, r=4

Hence the required parametric equation is,

[tex]\begin{gathered} x=4\left(θ−sinθ\right) \\ y=4\left(1−cosθ\right) \end{gathered}[/tex]

Answer is:

[tex]\begin{gathered} x=4\left(θ−sinθ\right) \\ y=4\left(1−cosθ\right) \end{gathered}[/tex]
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