Classical mechanics

I would like for you to show me all of your work/calculations and the correct answer to each problem.

51. What is the gravitational potential energy, relative to the ground, of a 1.0-kg box at the top of a 50-m building?

55. A 0.20-kg stone is thrown vertically upward with an initial velocity of 7.5 m/s from a starting point of 1.2 m above the ground. (A) What is the potential energy of the stone at its maximum height relative to the ground? (B) What is the change in the potential energy of the stone between its launch point and its maximum height?

57. The floor of the basement of a house is 3.0 m below ground level, and the floor of the attic is 4.5 m above ground level. (A) If an object in the attic were brought to the basement, the change in potential energy will be greatest relative to which floor, (1) attic, (2) ground, (3) basement, OR (4) all the same? Why?

(B) What are the respective potential energies of 1.5-kg objects in the basement and attic, relative to ground level?

(C) What is the change in potential energy if the object in the attic is brought to the basement?

67. A 0.300-kg ball is thrown vertically upward with an initial speed of 10.0 m/s. If the initial potential energy is taken as zero, find the ball's kinetic, potential, and mechanical energies (A) at its initial position, (B) at 2.50 m above the initial position, and (C) at its maximum height.

77. A 28-kg child slides down a playground slide from a height of 3.0 m above the bottom of the slide. If her speed at the bottom is 2.5 m/s, what is the work done by non-conservative forces?

81. If you check your electricity bill, you will note that you are paying the power company for so many kilowatt-hours (kWh). Are you really paying for power? Explain. Also, convert 2.5 kWh to J.

85. A girl consumes 8.4 x 10 J (2000 food calories) of energy per day while maintaining a constant weight. What is the average power she produces in a day?

87. The two 0.50-kg weight of a cuckoo clock descend 1.5 m in a three-day period. At what rate is gravitational potential energy decreased?

91. The Gossamer Albatross, a human-powered aircraft that requires the pilot to pedal, flew across the English Channel on June 12th, 1979, in 2 h and 49 minutes. If the average power needed to keep the aircraft flying is 0.30 hp, how much energy did the pilot use during the flight?

93. A sleigh and driver with a total mass of 120 kg is pulled up a hill with a 15 degrees incline by a horse. (A) If the overall retarding frictional force is 950 N and the sled moves up the hill with a constant velocity of 5.0 km/h, what is the power output of the horse? (Express in horsepower, of course. Note the magnitude of your answer, and explain.)

(B) Suppose that in a spurt of energy, the horse accelerates the sled uniformly from 5.0 km/h to 20 km/h in 5.0 s. What is the horse's maximum instantaneous power output? Assume the same force of friction.