Question

Two object of mass 100g. And200g are moving along the same line in the same Direction with velocity 2m/s and 1m/s they collide after collision the first body moves at velocity of1.67m/s in the same direction determine the velocity of the second body

Answer 1

Answer:

$\large\mathbf\color{Brown}\underline{\underline{Question:}}$

$\textsf{Two object of mass 100 g and 200 g are}$

$\textsf{moving along the same line in the same}$

$\textsf{direction with velocity 2 m/s and 1 m/s.}$

$\textsf{They collide after collision the first}$

$\textsf{body moves at velocity of 1.67 m/s}$

$\textsf{in the same direction determine}$

$\textsf{the velocity of the second body.}$

$\large\mathbf\color{cyan}\underline{\underline{Given:}}$

$\textsf{Mass of the first object = 100 g}$

$\textsf{Mass of the second object = 200 g}$

$\textsf{Intial velocity of the first object = 2 m/s}$

$\textsf{Initial velocity of the second object = 1 m/s}$

$\textsf{Final velocity of the first object = 1.67 m/s}$

$\large\mathbf\color{green}\underline{\underline{To\:find:}}$

$\textsf{Final velocity of the second object}$

$\large\mathbf\color{blue}\underline{\underline{Taken:}}$

$\textsf{To find the final velocity of the second object.}$

$\textsf{Use this formula:}$

$\mapsto\bold{m1v1+m2v2=m1v3+m2v4}$

$\bold{Where,}$

$\textsf{m1=Mass of the first object}$

$\textsf{m2=Mass of the second object}$

$\textsf{v1=Initial velocity of the first object}$

$\textsf{v2=Initial velocity of the second object}$

$\textsf{v3=Final velocity of the first object}$

$\textsf{v4=Final velocity of the second object}$

$\textsf{In the following we have to find the final}$

$\textsf{velocity of the second object or v4}$

$\large\mathbf\color{magenta}\underline{\underline{Concept:}}$

$\textsf{Use the formula to get the final velocity of the}$

$\textsf{second object after the collision between the}$

$\textsf{first object.}$

$\large\mathbf\color{red}\underline{\underline{Solution:}}$

$\bold{Taken,}$

$\bold{m1v1+m2v2=m1v3+m2v4}$

$\Rightarrow\bold{100g×2m/s+200g×1m/s=100g×1.67+200g×v4}$

$\Rightarrow\bold{200+200=167+200v4}$

$\Rightarrow\bold{400=167+200v4}$

$\Rightarrow\bold{400-167=200v4}$

$\Rightarrow\bold{233=200v4}$

$\Rightarrow\bold{\frac{233}{200}=v4}$

$\Rightarrow\bold{1.65m/s=v4}$

$\small\therefore\bold{The\:final\:velocity\:of\:the\:second\:object =1.65m/s}$

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So , the final velocity of the second object after collision is 1.65 m/s.

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$\large\mathbf\color{purple}\underline{\underline{Extra\:information:}}$

$\bold{Velocity=\frac{Displacement}{Time}}$

$\bold{Acceleration=\frac{Final\:velocity-Initial\:velocity}{Time\:taken}}$

HOPE IT HELPS YOU