Answer :
The expression for the velocity of the system after the collision is Vf = -2.420i - 3.471Ĵ
from conservation of linear momentum.
Pi = Pf
([tex]M_{C}[/tex]) (-vci) + (mt) (-vtj) = (mctmt)vf
(1456) (-5.5i) + (1852) (-6.2Ĵ)
= (1456 + 1852) Vf
Vf= [tex]\frac{1}{3308}[/tex] (8008 î - 11482.4j)
Vf = -2.420i - 3.471Ĵ
Both mass and velocity are directly proportional to momentum. Increasing either mass or velocity increases the object's momentum proportionally. Doubling the mass or velocity doubles the momentum. When matter collides, momentum is transferred collectively rather than velocity as a single component.
When a heavy mass meets a small mass the collective momentum increases, but the collective velocity decreases. A fast-moving object with high momentum transfers more energy to a slow-moving object than vice versa. After a collision, an object with a slow initial velocity moves away with a higher velocity and momentum than an object with a faster initial velocity.
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