Amodel train engine was moving at a constant speed on a straight horizontal track. as the engine movedâ along, a marble was fired into the air by a spring in theâ engine's smokestack. theâ marble, which continued to move with the same forward speed as theâ engine, rejoined the engine 1 sec after it was fired. the measure of the angle theâ marble's path made with the horizontal was 57 degrees. use the information to find how high the marble went and how fast the engine was moving.

Apulley with mass mp and a radius rp is attached to the ceiling, in a gravity field of 9.81 m/s2 and rotates with no friction about its pivot.

4r-134a enters the condenser of a residential heat pump at 800 kpa and 50°c at a rate of 0.022 kg/s and leaves at 750 kpa subcooled by 3°c. the refrigerant enters the compressor at 200 kpa superheated by 4°c determine (a) the isentropic efficiency of the compressor, (b) the rate of heat supplied to the heated room, and (c) the cop of the heat pump. also, determine (d) the cop and rate of heat supplied to the heated room if this heat pump operated on the ideal vapor-compression cycle between the pressure limits of 200 and 800 kpa. (0.757, 4.37 kw, 5.12, 6.18, 3.91 kw)

What practical value did astronomy offer to ancient civilizations?