SOLUTION: A particle is moving around the ellipse 4x^2+16y^2 = 64. At any time t its x and y coordinates are given by x = 4cos(t) and y = 2sin(t). At what rate is the particle's distance to

Question 994014: A particle is moving around the ellipse 4x^2+16y^2 = 64. At any time t its x and y coordinates are given by x = 4cos(t) and y = 2sin(t). At what rate is the particle's distance to the origin changing when t = π/4?
I know this is a related rates problem. But I don't know how to set this problem up in order to solve.
Thank you
Answer by KMST(5328) (Show Source): You can put this solution on YOUR website!
I would think this is a calculus problem.
The distance to the origin as a function of (time) is

The function showing the rate of change at time is
, and it can be calculated using the chain rule
with and
, and

Applying the chain rule again, and again, to both terms:
and
.
So, , and
.
Substituting the expression for ,

For ,
-->-->-->
-->-->-->-->
RELATED QUESTIONS
The x- and y-coordinates of moving particle are given by the parametric equation x =... (answered by Fombitz,ikleyn)

The x- and y-coordinates of moving particle are given by the parametric equation x =... (answered by Fombitz)

A particle moves along a line so that its position at any time t>=0 is given by s(t) =... (answered by Alan3354)

The x- and y-coordinates of a moving particle are given by two parametric equations. x = (answered by Fombitz)

Please help me with this problem: A particle moves along the x axis so that its velocity (answered by Fombitz,robertb)

Consider a particle moving along the x-axis where x(t) is the position of the particle at (answered by solver91311)

can someone show me how to do this problem: Suppose that the speed (in m/sec) of a... (answered by Edwin McCravy)

A particle is moving in the positive direction, away from the origin along the graph of y (answered by ikleyn)

A particle is moving according to an equation of motion. Its position after t seconds is... (answered by ikleyn)