Question

3.19 * (a) We know that the path of a projectile thrown from the ground is a parabola (if we ignore air resistance). In the light of the result (3.12), what would be the subsequent path of the CM of the pieces if the projectile exploded in midair? (b) A shell is fired from level ground so as to hit a target 100 m away. Unluckily the shell explodes prematurely and breaks into two equal pieces. The two pieces land 102 Chapter 3 Momentum and Angular Momentum at the same time, and one lands 100 m beyond the target. Where does the other piece land? (c) Is the same result true if they land at different times (with one piece still landing 100 m beyond the target)?

Answer 1

The centre of mass R moves exactly (1) as if it were a single particle of mass M, subject to the net external force on the system. Initially, the object is not exploded. Hence, the object is moving in the path of a parabola. When the projectile explodes by the external force on the system, centre of mass is same. therefore, the centre of mass of the pieces continues to move in the same parabolic path. Initial target of the projectile is at loom from the firing. Let the initial mass of projectile be m. As the centre of mass continues the same parabolic path, therefore when the two pieces reach the ground, the CM of \r\n The pieces will be at loom from the firing. X_cm = 100m And the first piece (and at a distance 100 m beyond the target. First piece is at a distance from the point of firing is, x_1 = 100 m + 100m