A body of mass m is projocted al an angle of 45^∘ with the horizontal with velocity v. If air re

step 1 Hello dear students here we have a question from two -dimensional motion. A body of mass M is pr

A body of mass m is projocted al an angle of 45^∘ with the...

A body of mass $m$ is projocted al an angle of $45^{\circ}$ with the horizontal with velocity $v$. If air resistanec is negligible, then total change in momentum when it strikes the ground is
(a) $2 \mathrm{mv}$
(b) $\sqrt{2} m$
(c) $m N$
(d) $m v / \sqrt{2}$

Key Concepts

Vector Addition in Momentum Analysis

Since momentum is a vector quantity, any calculation of change in momentum must take into account both its magnitude and direction. This means that the overall momentum change is obtained by vectorially adding the changes in its individual components, such as the unchanged horizontal component and the reversed vertical component, which is crucial for accurately quantifying the net change in momentum upon impact.

Impulse

Impulse is defined as the change in momentum of an object and it is equivalent to the force applied multiplied by the time over which the force acts. In collision problems, like a projectile striking the ground, impulse helps quantify the total change in momentum during the impact event, making it a key concept in understanding how momentum transforms during such interactions.

Projectile Motion

Projectile motion refers to the two-dimensional motion of an object under the influence of gravity alone, after it has been launched at an initial angle. In the absence of air resistance, the horizontal component of velocity remains constant while the vertical component is uniformly accelerated by gravity. This symmetry in motion (especially for a 45° launch) allows for predictable behavior at launch and impact, which is key when analyzing momentum changes.

Momentum

Momentum is a measure of the motion of an object and is calculated as the product of its mass and velocity. Being a vector quantity, momentum has both magnitude and direction. Understanding momentum is crucial because any change in the speed or direction of the velocity results in a change in the momentum, which is a core concept when analyzing collisions or impacts.

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