# What was the initial velocity of a body of mass 10 kg if it sticks to a a stationary body of mass 5 kg and the two move together at 4 m/s.

justaguide | College Teacher | (Level 2) Distinguished Educator

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When two masses collide and stick to each other it is a perfectly inelastic collision. Here the total momentum is not conserved, but the total energy is conserved.

The kinetic energy is given by 0.5*m*v^2

Initially we have the mass of 10 kg moving. Let its velocity be V.

Therefore its kinetic energy is 0.5*10* V^2

The kinetic energy of the mass of 5 kg is 0.

Total kinetic energy in the system is 0.5*10* V^2

After the collision , the two masses move at 4 m/s. The kinetic energy in the system is .5* 15* 4^2

Equate .5* 15* 4^2 to 0.5*10* V^2

=> .5* 15* 4^2 = 0.5*10* V^2

=> 15* 16 = 10*V^2

=> V^2 = 15*16/10 = 24

=> V = sqrt 24

Therefore the velocity of the 10 kg mass initially was sqrt 24 m/s.

syedajmain | Student | (Level 3) Honors

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The answer to this problem is 6 m/s...but I am not getting the clue of how...I am stuck..pls help me with more accurate answer. Thank you..