In space (no gravity or friction), you throw a ball with mass 0.1 kg at a target with mass 1 kg. you throw the ball at a speed of 3 m/s. when the ball impacts the target, it sticks to it and they drift off together. 1) how much energy is in the translational energy of the block+ball system after the collision?

It is not specified but I assume the target is initially at rest.

We can use the conservation of momentum to calculate the final velocity of the ball+block system. The initial momentum is the one of the ball, since the target is at rest:

where  is the mass of the ball and  is the initial velocity of the ball.

The final momentum is instead:

where  is the mass of the block. For the conservation of momentum,

so we can find the final velocity of the ball+block system:



And the translational energy of the block+ball system after the collision is equal to its kinetic energy: