A spherical cannonball of mass 2M is launched with an initial velocity v0 at an angle of 45° above the horizontal. There is an explosive charge between the two halves of the cannonball which is detonated when the cannonball has reached the highest point of its trajectory. One half of the cannonball (mass M) is propelled backwards exactly along the original trajectory and lands back in the cannon (good trick!). Ignore air resistance for this problem.
(a) Assuming level terrain, find the range of the center of mass of the system, i. e., how far away from the cannon does the center of mass of the system land?
(b) Find the velocity of the second half of the cannonball (the one that doesn't land back in the cannon) immediately after the explosion.
(c) How far away from the cannon does the second half of the cannonball land?