Consider an object moving in the plane whose location at time t seconds is given
ID: 2869035 • Letter: C
Question
Consider an object moving in the plane whose location at time t seconds is given by the parametric equations:
x(t)=4cos(?t)
y(t)=3sin(?t).
Assume the distance units in the plane are meters.
(a) The object is moving around an ellipse (as in the previous problem) with equation:
x^2/a^2 + y^2/b^2 = 1
where a= ______ and b= .___________
(b) The location of the object at time t=1/3 seconds is
( , ).
(c) The horizontal velocity of the object at time t is x ' (t)= ____ m/s.
(d) The horizontal velocity of the object at time t=1/3 seconds is ____ m/s.
(e) The vertical velocity of the object at time t is y ' (t)= ____m/s.
(f) The vertical velocity of the object at time t=1/3 seconds is _____ m/s.
(g) The slope of the tangent line at time t=1/3 seconds is _____.
(h) Recall, the speed of the object at time t is given by the equation:
s(t)=? [x '(t)]2 + [y ' (t)]2m/s.
The speed of the object at time t=1/3 seconds is ._________
(i) The first time when the horizontal and vertical velocities are equal is time t= ._______________
(j) Let Q be the position of the object at the time you found in part (i). The slope of the tangent line to the ellipse at Q is ______________
Explanation / Answer
Below link :
http://imgur.com/vo7RfRU