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.