## Elastic Collision Formula :

The Elastic Collision formula is the mass of 1^{st} body m_{1(kg/s)} in kilogram per second multiply the initial velocity of 1^{st} body u_{1(}_{m/s)} in meter per second multiply mass 2^{nd} body m_{2(kg/s)} in kilogram per second multiply the initial velocity of the second body u_{2}_{ (m/s)} in meter per second is equal to the mass of the 1^{st} body m_{1(kg/s)} in kilogram per second and multiply final velocity of the first body V_{1} _{(}_{m/s)} in meter per second and addition of mass of the 2^{nd} body m_{2(kg/s)} in kilogram per second final velocity of second body V_{2(kg/s)} in kilogram per second. Hence Elastic collision formula can be written as,

**m _{1(kg/s)}* u_{1(}_{m/s)} +m_{2(kg/s)} *u_{2}_{ (m/s)} =m_{1(kg/s)}* V_{1} _{(}_{m/s)} +m_{2(kg/s)}* V_{2(kg/s)}**

Where,

m1→ mass of 1st body in kg/s

m2→ mass of 2nd body in kg/s

u1→ initial velocity of 1st body in m/s

u2 → initial velocity of the second body in m/s

v1 → final velocity of the first body in m/s

v2 i→ final velocity of the second body in m/s

## Sample Sums :

### Sum1 :

Calculate the velocity of the ball of mass 8 Kg ball after the collision? If the ball has a mass 6 Kg and moving with the velocity of 15 m/s collides with a stationary ball of mass 9 kg and comes to rest.

### Solution :

Given parameters are

Mass of 1 st ball m_{1} is 6kg

The initial velocity of the first ball u_{1} is 15m/s

The mass of the second ball m_{2} is 9kg

The initial velocity of the second ball u_{2} is 8

The final velocity of the first ball v_{1} is 0

Final Velocity of the second ball v_{2} =?

1/2 m_{1}* u_{1}^{2} +1/2m_{2}* u_{2}^{2}=1/2m_{1}* V_{1}^{2} +1/2m_{2} *V_{2}^{2}

(1*6×*(15)^{2})/2+(1*9*8)/2=(1*6*0)/2+(1*9)/2* V_{2}^{2}

4086=4.5

=908

V^{2}= 908

V= √908

= 30.13 m/s

### Sum 2 :

Calculate the final velocity of first body ? In a 20 Kg block is moving with an initial velocity of 25 m/s with 9 Kg wooden block moving towards the first block with velocity 9 m/s. The second body comes to rest after the collision.

### Solution :

Given parameters are

Mass of 1 st ball m_{1} is 20kg

The initial velocity of the first ball u_{1} is 25m/s

The mass of the second ball m_{2} is 9kg

The initial velocity of the second ball u_{2} is 9 m/s

The final velocity of the first ball v_{1} is 0

Final Velocity of the second ball v_{2} =?

m_{1}* u_{1} +m_{2}* u_{2}=m_{1}* V_{1} +m_{2}* V_{2}

(20 *25)+(9 *9)=(20 *v1)+(9 *0)

581=20V_{1} +0

V_{1}=29.05

V_{1}=29.05 m/s