A body is projected vertically upwards from the surface of the earth with a velocity equal to half the escape velocity. If R is the radius of the earth, maximum height attained by the body from the surface of the earth is :
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- Find the escape velocity ve for an object of mass m that is initially at a distance R from the center of a planet of mass M. Assume that R≥Rplanet, the radius of the planet, and ignore air resistance. Express the escape velocity in terms of R, M, m, and G, the universal gravitational constant.A satellite has a mass of 5850 kg and is in a circular orbit 4.10 × 105 m above the surface of a planet. The period of the orbit is 2.00 hours. The radius of the planet is 4.15 × 106 m. (a) Find the mass of the planet,(b) the energy of the orbit, and (c) the escape velocity from this orbit. If the speed of the satellite is increased by 20% what would be the maximum distance above the planet? Needs Complete typed solution with 100% accuracy.Zero, a hypothetical planet, has a mass of 4.5 x 1023 kg, a radius of 3.2 x 106 m, and no atmosphere. A 10 kg space probe is to be launched vertically from its surface. (a) If the probe is launched with an initial kinetic energy of 5.0 x 107 J, what will be its kinetic energy when it is 4.0 x 106 m from the center of Zero? (b) If the probe is to achieve a maximum distance of 8.0 x 106 m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero?
- A spacecraft is launched from Cape Canaveral to a 28.5° inclined circular orbit of altitude h = 400 km. We want to reach the ISS, which orbit has the same altitude but is inclined at 51.6°. Explain what solutions are possible for this operation, and determine (using calculations) which is the most economical.If you took the Earth and reduced its radius to one fourth its current size, what would the escape velocity from the Earth be?(a) What is the escape speed on a spherical asteroid whose radius is 803 km and whose gravitational acceleration at the surface is 1.75 m/s2? (b) How far from the surface will a particle go if it leaves the asteroid's surface with a radial speed of 1330 m/s? (c) With what speed will an object hit the asteroid if it is dropped from 1811 km above the surface?
- when we calculate escape speeds, we usually do so with the assumption that the object from which we are calculating escape speed is isolated. This is, of course, generally not true in the solar system. Show that the escape speed at a point near a system that consists of two stationary massive spherical objects is equal to the square root of the sum of the squares of the escape speeds from each of the two objects considered individually.Two Earth satellites, A and B, each of mass m, are to be launched into circular orbits about Earth's center. Satellite A is to orbit at an altitude of 5390 km. Satellite B is to orbit at an altitude of 22500 km. The radius of Earth REis 6370 km. (a) What is the ratio of the potential energy of satellite B to that of satellite A, in orbit? (b) What is the ratio of the kinetic energy of satellite B to that of satellite A, in orbit? (c) Which satellite (answer A or B) has the greater total energy if each has a mass of 11.7 kg? (d) By how much?The escape velocity from the surface of planet A is 5700 m/s. Planet B has the same density but the radius is 1/3 that of planet What is the escape velocity from the surface of planet B in m/s?
- A satellite orbits a planet of unknown mass in a circle of radius 2 × 107 m. The magnitude of the gravitational force on the satellite from the planet is F = 80 N. a) What is the kinetic energy of the satellite in this orbit? b) What would F be if the orbit radius were increased to 3 x 107 m?SSM (a) What is the escape speed on a spherical asteroid whose radius is 500 km and whose gravitational acceleration at the surface is 3.0 m/s2? (b) How far from the surface will a particle go if it leaves the asteroid’s surface with a radial speed of 1000 m/s? (c) With what speed will an object hit the asteroid if it is dropped from 1000 km above the surface?Zero, a hypothetical planet, has a mass of 4.7 x 1023 kg, a radius of 3.2 x 106 m, and no atmosphere. A 10 kg space probe is to be launched vertically from its surface. (a) If the probe is launched with an initial kinetic energy of 5.0 x 107 J, what will be its kinetic energy when it is 4.0 x 106 m from the center of Zero? (b) If the probe is to achieve a maximum distance of 8.0 x 106 m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero? (a) Number: i Units: (b) Number: i Units: