Question

Suppose that the position of one particle at time t is given by x1 = 5 sin(t), y1 = 2 cos(t), 0 ≤ t ≤ 2π and the position of a second particle is given by x2 = −5 + cos(t), y2 = 1 + sin(t), 0 ≤ t ≤ 2π.If so, find the collision

Answer 1

To find the collision between two particles, set their x-coordinates equal to each other and solve for t. The radii of the circles of motion for both particles can be found by comparing their equations to the general equation for a circle. The x- and y-coordinates of the center of mass can be found by taking the average of the x-coordinates and the average of the y-coordinates of both particles.

Step-by-step explanation:

To find the collision between two particles, we need to find the time at which their positions are the same. Given the positions of particle 1 and particle 2, we can set their x-coordinates equal to each other and solve for t: 5sin(t) = -5 + cos(t). We then solve this equation to find the time of collision. Once we have the time, we can substitute it back into either particle's position equation to find the position of the collision.

We can also find the radii of the circles of motion for both particles by looking at their x and y coordinates. For particle 1, the x-coordinate equation is x1(t) = 5sin(t) and for particle 2, the x-coordinate equation is x2(t) = -5 + cos(t). By comparing these equations to the general equation for a circle, x = Rcos(t), we can see that the radius of the circle for particle 1 is 5 and for particle 2 it is 1.

To find the x- and y-coordinates of the center of mass, we need to find the average of the x-coordinates and the average of the y-coordinates of both particles. The x-coordinate of the center of mass is (x1(t) + x2(t))/2 and the y-coordinate of the center of mass is (y1(t) + y2(t))/2.