A shell is fired from a cannon with velocity v ms^-1 at an angle θwith the horizontal direction

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A shell is fired from a cannon with velocity v ms^-1 at an...

A shell is fired from a cannon with velocity $v \mathrm{~ms}^{-1}$ at an angle $\theta$ with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass, One of the pieces retraces its path to the cannon and the speed in $\mathrm{m} / \mathrm{s}$ of the piece immediately after the explosion is (a) $3 v \cos \theta$ (b) $2 v \cos \theta$ (c) $\frac{3 \mathrm{~V}}{2} \cos \theta$ (d) $\frac{\sqrt{3} v \cos \theta}{2}$

A shell is fired from a cannon with velocity $v \mathrm{~ms}^{-1}$ at an angle $\theta$ with the horizontal direction. At the highest point in its path it explodes into two pieces of equal mass, One of the pieces retraces its path to the cannon and the speed in $\mathrm{m} / \mathrm{s}$ of the piece immediately after the explosion is
(a) $3 v \cos \theta$
(b) $2 v \cos \theta$
(c) $\frac{3 \mathrm{~V}}{2} \cos \theta$
(d) $\frac{\sqrt{3} v \cos \theta}{2}$

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Key Concepts

Projectile Motion

Projectile motion is the two-dimensional motion of an object under the influence of gravity. The trajectory is parabolic, with the horizontal component of velocity remaining constant and the vertical component being affected by gravitational acceleration. At the highest point of the trajectory, the vertical velocity is zero, so the motion is entirely horizontal.

Conservation of Momentum

Conservation of momentum is a fundamental principle of physics stating that the total momentum of an isolated system remains constant if no external forces act on it. In the context of an explosion, even though internal forces generate changes in speed and direction of individual fragments, the vector sum of the momenta of all fragments is equal to the momentum of the original object just before the explosion.

Center-of-Mass Motion in Explosive Events

When an object explodes, the center of mass of the resulting pieces continues to move with the same velocity as the original object had prior to the explosion. This means that, despite changes in individual fragment speeds due to the explosion, the overall trajectory of the system’s center of mass is unaffected by the internal forces involved in the explosion.

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