Imagine an astronaut in a spaceship so far away from any celestial objects that we can neglect the effects of gravity. Assume that there is no air resistance. The astronaut attaches a rock to a rope and starts rotating it fast in a circle.

Ok i am attempting to my niece attach a galvanized wire (like a tether for a dog) at the corner of two fences, making a tightwire if you will and we drilled a hole in a softball and she hits it. the ? and problem is that we can not get the wire taunt enough where it doesnt sag after hitting the ball once, and the wire sags and wobbbles. its a 15 ft rubber covered galvanized wire and one can adjust the length of the placing of the wire by having it make the corner of 2 fences become a it can be adjusted, however, with all our human strength and pliers we could not make it taunt as possible. is there anything other that attaching it to a car to do this. sorry abt the length but it would mean the world to my niece if i could solve this came up with the entire idea herself, and she is 14 and paid for the wire and did as much work as i did drilling a hole through a softball wide enough for attaching piece at each end of the wire that clips on to the fence. . any ideas welcome if serious. but awesome if it is a fact. much obliged. bucky bukowski buckman

An engineer designs a roller coaster so that a car travels horizontally for 162 ft, then climbs 127 ft at an angle of 31.0° above the horizontal. it then moves 127 ft at an angle of 46.0° below the horizontal. if we take the initial horizontal motion of the car to be along the +x-axis, what is the car's displacement? (give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the +x-axis.)

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?