(20pts) Consider a disk of mass m and radius r, as shown below. It is resting on a horizontal surface. A particle of mass m strikes the disk at point P with a velocity v, and sticks to the disk. Just after the impact, the disk along with the embedded particle, starts rolling without slipping on the horizontal surface. During the impact, the ground provides a horizontal linear impulse F as shown below. (The moment of inertia of a uniform disk about its center Cis %mrz) a. (7pts) Write the linear impulse-momentum equation of the impact. (7pts) Write the angular impulse-momentum equation of the impact about a suitable reference point. c. (6pts) Determine an expression of the linear impulse F and the angular velocity w of the disk just after impact