11. a skateboarder with a mass of 35 kg ends up with a final velocity of 7 m/s after a push of 380
joules of work. what was the skateboarder's initial velocity?

The law of conservation of energy. The energy due to work performed on the skateboarder is converted into kinetic energy such that:

Work=Kinetic Energy

So 380=(1/2)(35)(7-Vo). I don’t have a calculator so..

Assumptions we made:
No energy loss, all work went into the energy of motion of the skateboarder. In the real world, this is not possible because some of the energy can be loss through friction of the skateboarder to the ground etc.