Please answer all parts in detail

Problem Solving Assignment 12 i/1/24, 12:10 PM Upeak o a. Consider the moment the projectile is launched. It starts from the origin with a speed V,. Express the initial position To and the initial momentum P, as vectors in terms of the given quantities v,, 6, m, and g, using 7 and 7 unit vector notation either is zero, say so. Include a sketch with the two vectors drawn tail-to-tail. b. Calculate the initial rotational momentum f}o in two steps: i. find the magnitude using |Eo| = |7,||B,| sin expressing your answer in terms of the given quantities ,, 6, m, and g, and ii. find 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 7 and the final momentum D s as vectors in terms of the given quantities v,, 6, m, and g, using 7 and 3 unit vector notation, if either is zero, say so. Include sketch with the two vectors drawn tail-to-tail. d. Calculate the final rotational momentum ]jf in two steps: i. find the magnitude using |L| = |7'||D ;| sin expressing your answer in terms of the given quantities Vo, 6, 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? Ifit is, explain why it must be conserved. If not explain what torque is causing the rotational momentum to change. 4. Dueling Mass-Spring Systems Consider the four block-and-spring(s) systems shown below. Each block moves on a horizontal, frictionless table. The blocks a have the same mass m, and all of the springs are identical and ideal, with spring constant k. At the instant shown, each block i released from rest a distance A to the right of its equilibrium position (indicated by the dashed line). https://ilearn.laccd.edu/courses/270459/assignments/6553721