A projectile of mass M is fired from the ground. If it did not explode, its range would be R . At its highest point, it explodes into two fragments of masses M 3 and 2M 3 . The lighter fragment comes to rest immediately after the explosion and falls vertically downwards. The distance from the launch point where the heavier fragment lands is

Step-by-step solution

The explosion is caused by internal forces, which do not change the trajectory of the center of mass of the system. The center of mass will continue its original parabolic path and land at a distance R from the launch point. The lighter fragment of mass M 3 comes to rest at the highest point and falls vertically. The horizontal distance of the highest point from the launch point is R 2 . Let the heavier fragment of mass 2M 3 land at a distance x from the launch point. Applying the formula for the position of the ce