Question

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

Answer 1

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.

Step-by-step 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,

`\begin{gathered} x=r\left(θ−sinθ\right) \\ y=r\left(1−cosθ\right) \end{gathered}`

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,

`\begin{gathered} x=4\left(θ−sinθ\right) \\ y=4\left(1−cosθ\right) \end{gathered}`

Answer is:

`\begin{gathered} x=4\left(θ−sinθ\right) \\ y=4\left(1−cosθ\right) \end{gathered}`