An insulated beaker with negligible mass contains liquid water with a mass of 0.250 kg and a temperature of 84.4 ∘c .
how much ice at a temperature of -10.6 ∘c must be dropped into the water so that the final temperature of the system will be 21.0 ∘c ?
take the specific heat of liquid water to be 4190 j/kg⋅k , the specific heat of ice to be 2100 j/kg⋅k , and the heat of fusion for water to be 3.34×10^5 j/kg .

Your starship, the aimless wanderer, lands on the mysterious planet mongo. as chief scientist-engineer, you make the following measurements: a 2.50-kg stone thrown upward from the ground at 14.0 m/s returns to the ground in 5.70 s ; the circumference of mongo at the equator is 2.20×10^5 km ; and there is no appreciable atmosphere on mongo. (a) the starship commander, captain confusion, asks for the following information: what is the mass of mongo? (b) if the aimless wanderer goes into a circular orbit 2.20×10^4 km above the surface of mongo, how many hours will it take the ship to complete one orbit? (c) an unmanned spacecraft is in a circular orbit around the moon, observing the lunar surface from an altitude of 44.0 km . to the dismay of scientists on earth, an electrical fault causes an on-board thruster to fire, decreasing the speed of the spacecraft by 23.0 m/s . if nothing is done to correct its orbit, with what speed (in km/h) will the spacecraft crash into the lunar surface?