Awell-greased, essentially frictionless, metal bowl has the shape of a hemisphere of radius 0.150 m. you place a pat of butter of mass 5.00×10−3kg at the rim of the bowl and let it slide to the bottom of the bowl. what is the speed of the pat of butter when it reaches the bottom of the bowl?

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?