Question

a marble is rolled on the floor in a straight line from one person to another person. the marble has a radius of 0.9 cm and there is a fixed point ( p ) located on the marble. let the person rolling the marble represent the origin. find parametric equations in terms of ( \theta ) describing the cycloid traced out by ( p ).

Explanation:

Step1: Recall the parametric equations for a cycloid

The parametric equations for a cycloid generated by a circle of radius \(r\) are \(x = r(\theta-\sin\theta)\) and \(y=r(1 - \cos\theta)\), where \(\theta\) is the angle of rotation of the circle.

Step2: Substitute the radius value

Given that \(r = 0.9\) cm.
For the \(x\) - coordinate: \(x=0.9(\theta-\sin\theta)\)
For the \(y\) - coordinate: \(y = 0.9(1-\cos\theta)\)

Answer:

The parametric equations are \(x = 0.9(\theta-\sin\theta)\) and \(y=0.9(1 - \cos\theta)\)