A body moves in the x-y plane such that x = Rcoswt and y=Rsinwt. Here x and y ar

Question

A body moves in the x-y plane such that x = Rcoswt and y=Rsinwt. Here x and y are the coordinates of the body, t is the time and R and w are constants. a. Eliminate t between these equations to find the equation of the curve in which the body moves. What is the curve? What is the meaning of the constant w? HINT: use a trigonometric relationship. b. Differentiate the equations for x and y with respect to the time to find the x and y components of the velocity of the body, vx and vy. Combine the two equations to find the magnitude and direction of v. Describe the motion of the body. c. Differentiate vx and vy with respect to the time to obtain the two acceleration components and then combine to find the magnitude and direction of the resultant acceleration.

Explanation / Answer

given
x= Rcoswt , y= Rsinwt
now
x2 +y2 = (Rcoswt)2 + (Rsinwt)2

or   x2 +y2 = R2

hence cuve is x2 +y2 = R2 , a circle of radius R

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