The pull of gravity (g) on Mars is 3.7 m/s2. If an astronaut on Mars lifts a 10 kg rock 1 m off the ground, just to see what’s under it, how much work has the astronaut performed?

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?

Ablue car pulls away from a red stop-light just after it has turned green with a constant acceleration of 0.5 m/s 2 . a green car arrives at the position of the stop-light 6.5 s after the light had turned green. if t = 0 when the light turns green, at what time does the green car catch the blue car if the green car maintains the slowest constant speed necessary to catch up to the blue car? answer in units of s.

Newton's law of cooling states that the rate of change in the temperature t(t) of a body is proportional to the difference between the temperature of the medium m(t) and the temperature of the body. that is, startfraction dt over dt endfraction equals upper k left bracket upper m left parenthesis t right parenthesis minus upper t left parenthesis t right parenthesis right bracket , where k is a constant. let kequals0.04 left parenthesis min right parenthesis superscript negative 1 and the temperature of the medium be constant, m(t) font size decreased by 3 equivalent font size decreased by 3 294 kelvins. if the body is initially at 369 kelvins, use euler's method with hequals0.1 min to approximate the temperature of the body after (a) 30 minutes and (b) 60 minutes.