A spring-loaded dart gun is used to shoot a dart straight up into the air, and the dart reaches a maximum height of 24 meters. The same dart is shot up a second time from the same gun, but this time the spring is compressed only half as far (compared to the first shot). How far up does the dart go this time (neglect friction and assume the spring obeys Hooke's law)

Acoal-fired plant generates 600 mw of electric power. the plant uses 4.8 x 10^6 kg of coal each day, and the heat of combustion of coal is 3.3x 10^7 j/kg. the steam that drives the turbines is at a temperature of 300° c, and the exhaust water is at 37° c. (a) what is the overall efficiency of the plant for generating electric power? (b) how much thermal energy is exhausted each day? (c) what is the change in entropy of the universe for this heat engine? (d) using the same heat reservoirs, what is the maximum possible (carnot) efficiency for a heat engine?

After a big snowfall, you take your favorite rocket-powered sled out to a wide field. the field is 195 m across, and you know that your sled accelerates at a rate of 3.65 m/s2 when the rocket is on. how much time will it take the sled to cross the field starting from rest, assuming the rocket is on the whole time?

An ideal polarizer with its transmission axis rotated 30 degrees to the vertical is placed in a beam of unpolarized light of intensity 10w/m^2. after passing through the polarizer, what is the intensity of the beam? a. 8.7 w/m^2 b. 7.5 w/m^2 c. 5.0 w/m^2 d. 10 w/m^2 e. 2.5 w/m^2