A firework of mass 0.25 kg is launched at an angle of 75 degrees above the horizontal, pointing due west. The initial speed of the firework is 69 m/s. At the top of its trajectory, it explodes into two pieces of equal mass. One of the pieces takes 2.1 s to fall to the ground, and lands on the ground a distance of 53 m due west from the launch position. Neglect air resistance.
(a) Find the velocity of both pieces just after the explosion.
(b) Where does the other piece land?
(c) Sketch a picture of the resulting motion and convince yourself that it is plausible.