Consider the motion of a projectile of mass m launched from the ground with an initial yelocity El}; at angle 9. as depicted below. In this problem we are going to study this motion through the lens of rotational momentum, I: by applying the denition I: = F X E3 where F is the position vector of the body with respect to the origin leg. the piyotl and 1:3 is the momentum of the object. Assume that the acceleration due to gravity is g. a. Consider the moment the projectile is launched. It starts from the origin with a speed UH. Express the initial position E, and the initial momentum EU as vectors in terms of the given quantities on, . 9, m, and g, using ; and} unit vector notation, if either is zero, say so. Include a sketch with the two vectors drawn tail-to-tail. [3. Calculate the initial rotational momentum EH in two steps: i. nd the magnitude using IEHI = IFHI lsl Sin ti? expressing your answer in terms of the given quantities E35,, m, and g, and ii. nd the direction using the right-hand- rule, expressing your answer in terms of a unit vector direction. c. The projectile lands a distance R away from the origin. Express the final position ry and the final momentum py as vectors in terms of the given quantities vo , 0, m, and g, using i and j unit vector notation, if either is zero, say so. Include a sketch with the two vectors drawn tail-to-tail. d. Calculate the final rotational momentum L in two steps: i. find the magnitude using IZyl = [ylIp, | sin ) expressing your answer in terms of the given quantities U. , 0, m, and g, and ii. find the direction using the right-hand- rule, expressing your answer in terms of a unit vector direction.e. Is the rotational momentum of the system of the projectile conserved? If it is, explain why it must be conserved. If not, explain what torque is causing the rotational momentum to change