please WRITE all equations used and circle final answer. draw diagrams and use equations covered in work, energy, and momentum.

1. a ballistic pendulum, a bullet with mass of 40.0 g is fired in to the catcher with mass of 600.0 g. The length of pendulum is 60.0 cm. After bullet embedded in to the catcher, total system rises to the angle of 50 degrees compare to perpendicular line. Find initial speed of the Bullet when it get fired by the gun. (a) Derive equation. (b) find magnitude of speed.(apply conservation of momentum and then conservation of energy)

2. a 900 g particle has velocity vx = -8.0 m/s at t = 2 s. Force Fx (t) = 50t2.e4t Newton is exerted on the particle between t = 2 s and t = 8 s. This force increases from 0.0N at t = 2 s to 15.0N at t = 5 s and then back to 0 N at t = 8 s. What is the particle's velocity at t = 8 s?