A body of mass 0.5 kg is projected under gravity with a...

A body of mass $0.5 \mathrm{~kg}$ is projected under gravity with a speed of $98 \mathrm{~m} / \mathrm{s}$ at an angle of $30^{\circ}$ with the horizontal. The change in momentum (in magnitude) of the body is (a) $24.5 \mathrm{~N}-\mathrm{s}$ (b) $49.0 \mathrm{~N}-\mathrm{s}$ (c) $98.0 \mathrm{~N}-\mathrm{s}$ (d) $50.0 \mathrm{~N}-\mathrm{s}$

A body of mass $0.5 \mathrm{~kg}$ is projected under gravity with a speed of $98 \mathrm{~m} / \mathrm{s}$ at an angle of $30^{\circ}$ with the horizontal. The change in momentum (in magnitude) of the body is
(a) $24.5 \mathrm{~N}-\mathrm{s}$
(b) $49.0 \mathrm{~N}-\mathrm{s}$
(c) $98.0 \mathrm{~N}-\mathrm{s}$
(d) $50.0 \mathrm{~N}-\mathrm{s}$

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Key Concepts

Momentum

Momentum is a physical quantity defined as the product of the mass of an object and its velocity. It is a vector quantity, meaning it has both magnitude and direction, and plays a central role in the analysis of motion and collisions in physics.

Impulse

Impulse refers to the change in momentum of an object when a force is applied over a period of time. According to the impulse-momentum theorem, the impulse applied to an object is equal to the change in its momentum. This concept is critical when analyzing how forces, such as gravity, affect the motion of projectiles.

Projectile Motion Decomposition

Projectile motion involves breaking the motion of an object into horizontal and vertical components. The horizontal component of velocity remains constant (in the absence of air resistance), while the vertical component is influenced by gravity. This decomposition helps in understanding how the momentum changes, particularly by examining how the vertical component of momentum is altered due to gravitational acceleration.

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