Final answer:
By using the conservation of momentum and considering that the final velocity of the combined masses at the point of collision is zero, the projectiles will land at the point of collision, which is halfway between the two launch sites, or D/2.
Step-by-step explanation:
To solve this problem, we need to apply the principle of conservation of momentum. Momentum is defined as the product of mass and velocity and, in an isolated system, the total momentum before collision is equal to the total momentum after collision.
Given that the projectiles are initially moving in opposite directions with the same speed and eventually stick together upon collision, the distance at which they land (x) depends on the masses of the projectiles and satisfies the equation m1v - m2v = (m1 + m2)vf, where v is the initial speed of each projectile and vf is the final velocity of the combined mass after the collision. Since the two projectiles stick together at the highest point, their final velocity right after the collision must be zero.
Using the conservation of momentum, we find that the combined mass will fall vertically downward after the collision. Therefore, the place they will land is exactly at the point of collision, which is D/2 from each launch site.