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.
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.