Where bearings are given, they are in degrees East of North (so North is 000, degrees,000∘, East is 090, degrees,090∘, South is 180, degrees,180∘and West 270, degrees,270 ∘). For the purposes of this exercise, assume the Earth is flat. a) In which direction would I have to travel in order to travel North (relative to a stationary observer) if I am swimming in a river with a current running 0, point, 40, m, s, to the power minus 1 ,0.40ms −1 to the East, and I can swim at 1, point, 5, m, s, to the power minus 1 ,1.5ms −1 relative to the water? Give your answer as a bearing (degrees clockwise from North) to 3 significant figures.

b) In which direction would I have to travel in order to travel North (relative to a stationary observer) if I am flying in a 15, k, m, h, to the power minus 1 ,15kmh −1 wind coming from the West and can fly at 90, k, m, h, to the power minus 1 ,90kmh −1 relative to the air? Give your answer as a bearing (degrees clockwise from North) to 3 significant figures.

c) How fast do I move Northwards over the ground in part (b)?

Air is held within a frictionless piston-cylinder container, which is oriented vertically. the mass of the piston is 0.45 kg and the cross-sectional area is 0.0030 m2. initially (state 1) the pressure of the gas is sufficient to support the weight of the piston as well as the force exerted by the atmospheric pressure ( 101.32 kpa). the volume occupied by the air within the cylinder in state 1 is 1.00 liter. one end of a spring (with spring constant k = 1000 n/m) is attached to the top of the piston, while the other end of the spring is attached to a stage that can move vertically. initially the spring is undeflected and therefore exerts no force. then the stage is then moved quasistatically downward a distance of 10.0 cm, at which point the system reaches state 2. the piston-cylinder is not insulated; rather it remains in diathermal contact with the surroundings, which are at a constant temperature of 300 k. what is the change of pressure within the container?

Aheat engine running backward is called a refrigerator if its purpose is to extract heat from a cold reservoir. the same engine running backward is called a heat pump if its purpose is to exhaust warm air into the hot reservoir. heat pumps are widely used for home heating. you can think of a heat pump as a refrigerator that is cooling the already cold outdoors and, with its exhaust heat qh, warming the indoors. perhaps this seems a little silly, but consider the following. electricity can be directly used to heat a home by passing an electric current through a heating coil. this is a direct, 100% conversion of work to heat. that is, 19.0 \rm kw of electric power (generated by doing work at the rate 19.0 kj/s at the power plant) produces heat energy inside the home at a rate of 19.0 kj/s. suppose that the neighbor's home has a heat pump with a coefficient of performance of 4.00, a realistic value. note: with a refrigerator, "what you get" is heat removed. but with a heat pump, "what you get" is heat delivered. so the coefficient of performance of a heat pump is k=qh/win. an average price for electricity is about 40 mj per dollar. a furnace or heat pump will run typically 200 hours per month during the winter. what does one month's heating cost in the home with a 16.0 kw electric heater? what does one month's heating cost in the home of a neighbor who uses a heat pump to provide the same amount of heating?

An object resting on a table weighs 100 n. with what force is the object pushing on the table? with what force is the table pushing on the object? explain how you got your answer.