Discuss elastic collision in two dimesnsion .

Explanation

As shown in figure , suppose a ball of mass `m_(1)` moving in X - direction with speed `v_(1i)` collides elastically with a stationary ball of mass `m_(2)` .
after the collision these ball move in the direction making angle `theta_(1) and theta_(2)` with the X - axis with velocities `v_(1f) and v_(2f)`
Momentum is conserved in collision ,
` :. ` Momentum before collision = momentum after collision
` :. m_(1)v_(1i) = m_(1)v_(1f) +m_(2)v_(2f) " "...(1) [ :. v_(2i)=0 ] `
Here , there are three equations (2) , (3) and (4) and from these unknown quantities can be determined .
usually the value of `m_(1),m_(2),v_(1i) and v_(2i)` are known , whereas four terms `v_(1f),v_(2f) and theta_(1) and theta_(2)` are quantities must be known as three equations can be give the values of only three unknown quantities .
If the motion in one dimension then unknown terms `v_(1f) and v_(2f)` are only be obtained because in this motion `theta_(1)=theta_(2) = 0 ` and hence unknown term can be known by the equations in one dimension .