Question

A ball A of mass M collides elastically with another identical ball B at rest as shown in figure. Initially velocity of ball A is u m/s. After collision ,

• A. speed of ball A is $ucos$$\theta$
• B. speed of ball B is $usin$ $\theta$
• C. velocity of ball A is $usi{n}^2\theta$ i + $usin$ $\theta cos\theta j$
• D. None of these

Answer 1

The correct option is C velocity of ball A is $usi{n}^2\theta$ i + $usin$ $\theta cos\theta j$

By momentum conservation, ball A will move at an angle $90-\theta$ above x axis since ball B will move at an angle $\theta$ below the x axis as it experiences force only in that direction and in elastic collision, the balls move perpendicular after collision.

Also, by momentum conservation $u=v_{1}sin\left(\theta \right)+v_{2}cos\left(\theta \right)$.

By energy conservation, $u^2=v_1^2+v_2^2$.

Solving the above two equations gives $v_1=usin\left(\theta \right)$

$V_B=uco{s}^2\theta i-ucos\theta sin\theta j$
$V_A=usi{n}^2\theta i+usin\theta cos\theta j.$