Group 2 Due Tuesday 23 Sep Projects be stapled together with no dog-eared corners. Unstapled projects will NOT be accepted. All the names of the particpants must be on the projects. Each member needs to fill out a group evaluation form each week. The form is NOT stapled to the project but handed in separately 1. Find the points of intersection of the polar curves r = 1 + cos(theta) and r= 3 cos(theta). 2. An ant crawls along the radius from the center to the edge of a circular disk of radius 1 meter, moving at a constant rate of 1 cm/sec. Meanwhile the disk is turning counterclockwise about its center at 1 revolution per second. a. Parameterize the motion of the ant b. Find the velocity and speed of the ant c. Determine the acceleration and the magnitude of the acceleration of the ant. 3. Is the point (-3, -4, 2) visible from the point (4, 5, 0) if there is an opaque ball of radius 1 at the orgin? 4. Find parametric equations of the path of a red dot on a circle of radius one as the circle rolls along the x-axis. Start the circle with the red dot on the bottom and with the red dot at the origin. [Hint suppose the cirle has rotated theta radians, where is the center? where is the red point relative to the center? (hint: Vector addition)] 5. The lines L1 and L2 are parallel and suppose the vectors u-hat = and v-hat = are unit vectors, what is the distance between the lines. L1: = <0,0,0>+t L2: = +t [If u-hat = <1,0,0> and v-hat = <0,0,1> then the distance is 1. If u-hat = <1,0,0> and v-hat = <-1,0,0> then the distance is 0.]