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Transcript
Figure P13.47
48. A satellite moves around the Earth in a circular orbit of radius r. (a) What is the
speed υi of the satellite? (b) Suddenly, an explosion breaks the satellite into two
pieces, with masses m and 4m. Immediately after the explosion, the smaller piece
of mass m is stationary with respect to the Earth and falls directly toward the Earth.
What is the speed υ of the larger piece immediately after the explosion? (c)
Because of the increase in its speed, this larger piece now moves in a new
elliptical orbit. Find its distance away from the center of the Earth when it reaches
the other end of the ellipse.
49. At the Earth’s surface, a projectile is launched straight up at a speed of 10.0 km/s.
To what height will it rise? Ignore air resistance.
Additional Problems
50. A rocket is fired straight up through the atmosphere from the South Pole, burning
out at an altitude of 250 km when traveling at 6.00 km/s. (a) What maximum
distance from the Earth’s surface does it travel before falling back to the Earth? (b)
Would its maximum distance from the surface be larger if the same rocket were
fired with the same fuel load from a launch site on the equator? Why or why not?
51. Review. A cylindrical habitat in space 6.00 km in diameter and 30.0 km long has
been proposed (by G. K. O’Neill, 1974). Such a habitat would have cities, land,
and lakes on the inside surface and air and clouds in the center. They would all be
held in place by rotation of the cylinder about its long axis. How fast would the