A shell is fired from a cannon with a velocity v at angle θwith horizontal. At the highest point

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A shell is fired from a cannon with a velocity v at angle...

A shell is fired from a cannon with a velocity $v$ at angle $\theta$ with horizontal. At the highest point, it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon. The speed of the other piece just after explosion is (a) $3 v \cos \theta$ (b) $2 v \cos \theta$ (c) $\frac{3}{2} v \cos \theta$ (d) $\frac{\sqrt{3}}{2} v \cos \theta$

A shell is fired from a cannon with a velocity $v$ at angle $\theta$ with horizontal. At the highest point, it explodes into two pieces of equal mass. One of the pieces retraces its path to the cannon. The speed of the other piece just after explosion is
(a) $3 v \cos \theta$
(b) $2 v \cos \theta$
(c) $\frac{3}{2} v \cos \theta$
(d) $\frac{\sqrt{3}}{2} v \cos \theta$

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Key Concepts

Projectile Motion

Projectile motion describes the trajectory of an object launched into the air, subject only to gravitational acceleration. At the highest point of its trajectory, the vertical component of the velocity becomes zero while the horizontal component remains constant, which is crucial in analyzing events such as explosions occurring at this point.

Conservation of Linear Momentum

The principle of conservation of linear momentum states that in the absence of external forces, the total momentum of a system remains constant. This concept is essential when analyzing explosions, where despite the internal forces acting during the break-up, the overall momentum of the fragments must equal the momentum of the original projectile.

Center of Mass Motion

The motion of the center of mass of a system is governed by the net external forces acting on it, and remains unchanged during an explosion. Even if the projectile splits into multiple pieces, the velocity of the center of mass remains the same as that of the original object before the explosion, allowing one to relate the momenta of the fragments to the original projectile’s motion.

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