Ball A moving at 12 m/s collides elastically | vedclass

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(B) In an elastic collision between two objects of equal mass where one is initially at rest,the two objects move at an angle of $90^\circ$ to each ot

Vedclass · Accepted Answer

$6$

Vedclass · Answer

(B) In an elastic collision between two objects of equal mass where one is initially at rest,the two objects move at an angle of $90^\circ$ to each other after the collision.Let the initial velocity of ball $A$ be $\vec{u}_A = 12 \hat{j} \ m/s$ (assuming the vertical axis is the $y$-axis).Since the collision is elastic and the masses are equal,the conservation of momentum and kinetic energy implies that the velocity vectors after collision $\vec{v}_A$ and $\vec{v}_B$ satisfy $\vec{v}_A \cdot \vec{v}_B = 0$.Given the geometry of the collision,ball $A$ strikes ball $B$ at an angle of $60^\circ$ with the vertical. The component of velocity along the line of impact (normal) is transferred to ball $B$,while the component perpendicular to the line of impact remains with ball $A$.The velocity component of $A$ along the normal (horizontal $x$-axis) is $v_{Ax} = 12 \sin(60^\circ) = 12 	imes \frac{\sqrt{3}}{2} = 6\sqrt{3} \ m/s$.The velocity component of $A$ perpendicular to the normal (vertical $y$-axis) is $v_{Ay} = 12 \cos(60^\circ) = 12 	imes \frac{1}{2} = 6 \ m/s$.In an elastic collision of equal masses,the velocity component along the line of impact is exchanged. Thus,after collision,the $x$-component of $A$'s velocity becomes $0$,and the $y$-component remains $6 \ m/s$.Therefore,the final velocity of ball $A$ is $6 \ m/s$.

Similar Questions

After a head-on elastic collision between two balls of equal masses,one is observed to have a speed of $3\,m/s$ along the positive $x$-axis and the other has a speed of $2\,m/s$ along the negative $x$-axis. What were the original velocities of the balls?

Assertion $(A)$: In an elastic collision between two bodies,the relative speed of the bodies after collision is equal to the relative speed before the collision.
Reason $(R)$: In an elastic collision,the linear momentum of the system is conserved.

In the elastic collision of objects,

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$A$ body of mass $m$ moving with velocity $v$ makes a head-on elastic collision with another body of mass $2m$ which is initially at rest. What is the loss in kinetic energy of the colliding body?

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