A particle of mass m is projected with a velocity 6 î+8 ĵ. Find the change in momentum when il j

step 1 Hello students. Here we have a question from projectile motion. A particle of mass M is projecte

A particle of mass m is projected with a velocity 6 î+8 ĵ....

A particle of mass $m$ is projected with a velocity $6 \hat{i}+8 \hat{j}$. Find the change in momentum when il just touches ground
(a) 0
(b) $12 \mathrm{~m}$
(c) $16 \mathrm{~m}$
(d) $20 \mathrm{~m}$

Key Concepts

Change in Momentum Calculation

The change in momentum is calculated as the difference between the final and initial momentum vectors. In the context of projectile motion where certain components may remain unchanged (like horizontal velocity) and others may reverse their direction (like vertical velocity due to gravity), this concept is vital for understanding the overall impact on the object’s momentum.

Projectile Motion

Projectile motion describes the movement of an object under the influence of gravity alone, after being projected. In this motion, the horizontal component of velocity remains constant while the vertical component is uniformly accelerated due to gravity, which is crucial in determining how momentum changes in different directions.

Vector Decomposition

Vector decomposition is the process of breaking a vector into its components along mutually perpendicular directions, typically horizontal and vertical. This method is essential in analyzing projectile motion, as it allows one to treat and calculate the effects of forces and accelerations separately along each axis.

Momentum

Momentum is a fundamental vector quantity in mechanics defined as the product of an object's mass and its velocity. It characterizes both the magnitude and direction of the motion, and it plays a key role in the analysis of dynamic systems, including collisions and projectile motion.

Impulse-Momentum Theorem

The impulse-momentum theorem states that the change in momentum of an object is equal to the impulse applied to it. This theorem connects force and time to momentum change and is critical when analyzing events where momentum is altered, such as when forces act during the projectile’s flight.

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