Asteroid A, with a mass of 10^13 kg, is traveling at the velocity of 50 km/s in the positive x-direction and entering the Asteroid Belt. The Asteroid Belt has a width of 10^6 km. The asteroids in the Asteroid Belt all have masses of about 10^13 kg each and are traveling with velocities of about 10 km/s in the positive y-direction. Assume that while traversing the Asteroid Belt, Asteroid A is going to collide with at least three other asteroids far apart from each other (it encounters a Family of Asteroids). Assume that all of the collisions happen in the x-y plane and that none of the asteroids are destroyed in the collisions. Is Asteroid A going to leave the Asteroid Belt? If so, how far off-course in the y-direction (it was originally traveling along the x-axis) is it located when it leaves the Asteroid Belt? How would your answers change if Asteroid A collided with more asteroids? Make any assumptions you think are reasonable about the collisions and state those assumptions. You can solve the problem analytically or numerically using your favorite software (Matlab, Mathematica, etc.). Graph the trajectory of Asteroid A