Consider an object describing an elliptical path in the plane given by r (t) =
(2 cos t, 6sin t), where t is in the interval [0, 2].
if the object is subjected to a field with a force given by the expression G (x, y) = (4xy, y^2), calculate the work done
by G to move the object along the trajectory from (2, 0) to (0, 6), in direct order.

Question

Consider an object describing an elliptical path in the plane given by r (t) =
(2 cos t, 6sin t), where t is in the interval [0, 2].
if the object is subjected to a field with a force given by the expression G (x, y) = (4xy, y^2), calculate the work done
by G to move the object along the trajectory from (2, 0) to (0, 6), in direct order.

anonymous · Answer

$$W = \int\limits Gdr$$

anonymous · Answer

just not sure which expression will make easyer to calculate the dot product, paramtric or cartesian.

anonymous · Answer

probably parametric

anonymous · Answer

I tried parametric, though it would be easier.

anonymous · Answer

Use Polar Coordinate
x(t)= 2 cos(t)
y(t)= 6 sin(t)
P = 4 x y
Q  = y^2
Compute
 P(x(t),y(t)) x'(t) + Q(x(t),y(t))x'(t)=120 cos(t) sin^2(t)
Integrate the last expression for t= to Pi/2 to obtain 40

anonymous · Answer

This Q(x(t),y(t))x'(t) should be Q(x(t),y(t))y'(t)