Can someone please explain what Gamma means in physics with regards to speed and time, and how the equation is done, and what it is useful for?

Atomic nuclei of almost all elements consist of

Simon is writing a story about an astronaut whose spacecraft has been boarded by space pirates. the astronaut has her lucky penny in her hand behind her back as the space pirates break into the control room. she has just locked the controls so that the ship is accelerating in the direction of the control room’s ceiling. simon wants the astronaut to use the penny to hit a button on the control panel to turn off the lights and escape. the button is located a short distance behind and below the astronaut’s hands. how should simon use the theory of relativity to describe what the astronaut must do in order to hit the button?

Aball is thrown horizontally from a cliff at 8m/s .in what direction is the ball moving 2s later?