As shown in the figure,a pendulum $A$ is released from an angle of $30^{\circ}$ with the vertical and strikes a pendulum $B$ of equal mass. After the collision,to what height (in $m$) will pendulum $A$ rise? Neglect the size of the pendulum and assume the collision is perfectly elastic.

$A$ mass $m_1$ moves with a great velocity. It strikes another mass $m_2$ at rest in a head-on collision. It comes back along its path with low speed after the collision. Then:

$A$ sphere of mass $M$ moving with velocity $u$ undergoes a perfectly elastic collision with a stationary sphere of mass $m$. If their velocities after the collision are $V$ and $v$ respectively,what is the value of $v$?

$A$ moving body with a mass $m_1$ and velocity $u$ strikes a stationary body of mass $m_2$. The masses $m_1$ and $m_2$ should be in the ratio $\frac{m_1}{m_2}$,so as to decrease the velocity of the first body to $\frac{2u}{3}$ and give a velocity of $v$ to $m_2$,assuming a perfectly elastic impact. Then,the ratio $\frac{m_1}{m_2}$ is

Discuss elastic collision in two dimensions.

Consider the situation as shown in the figure. The ball strikes the wall normally and the collision is elastic. The wall is moving with a velocity of $20 \ m/s$ to the right,and the ball is moving with a velocity of $10 \ m/s$ to the left. The mass of the ball is $500 \ g$. The change in the kinetic energy of the ball is $....J$.