A body is launched from the earth's surface at an angle a = 30° to the horizontal at a speed vo = 1.5GM Neglecting air resistance and earth's rotation. Find the height to which the body will rise. Here M is mass of earth and R the radius of earth.

A satellite of Mars, called Phobos, has an orbital radius of 9.4 ✕ 106 m and a period of 2.8 ✕ 104 s. Assuming the orbit is circular, determine the mass of Mars. (ans kg)

A coordinate system (in meters) is constructed on the surface of a pool table, and three objects are placed on the table as follows: a m, = 1.9-kg object at the origin of the coordinate system, a m, = 3.3-kg object at (0, 2.0), and a m, = 5.3-kg object at (4.0, 0). Find the resultant gravitational force exerted by the other two objects on the object at the origin. magnitude Your response differs from the correct answer by more than 10%. Double check your calculations. N direction 68.12 o above the +x-axis

Aliens declare war on Earth by dropping an asteroid on our planet.  The asteroid starts at rest from a distance of 37 x 106 m from the center of Earth.  Calculate the speed with which the asteroid hits Earth's surface, in km/s.  Use that G = 6.7 x 10-11 N m2 / kg2, MEarth = 6 x 1024 kg, and REarth = 6 x 106 m. (Please answer to the fourth decimal place - i.e 14.3225)

The radius Rh of a black hole is the radius of a mathematical sphere, called the event horizon, that is centered on the black hole. Information from events inside the event horizon cannot reach the outside world. According to Einstein's general theory of relativity, Rh = 2GM/c2, where M is the mass of the black hole and c is the speed of light. Suppose that you wish to study a black hole near it, at a radial distance of 48Rh. However, you do not want the difference in gravitational acceleration between your feet and your head to exceed 10 m/s2 when you are feet down (or head down) toward the black hole. (a) Take your height to be 1.5 m. What is the limit to the mass of the black hole you can tolerate at the given radial distance? Give the ratio of this mass to the mass MS of our Sun.

Please solve

A satellite moves in a circular orbit aroundthe Earth at a speed of 5.5 km/s.Determine the satellite’s altitude abovethe surface of the Earth. Assume theEarth is a homogeneous sphere of radius6370 km and mass 5.98 × 1024 kg. Thevalue of the universal gravitational constantis 6.67259 × 10−11 N · m2/kg2.Answer in units of km.

Earth’s gravitational field strength at the surface is 9.80 N/kg. Determine the distance, as a multiple of Earth’sradius, rE, above Earth’s surface at which the magnitude of the acceleration due to gravity is 3.20 N/kg.

A solid uniform sphere has a mass of 4.00 x 10* kg and a radius of 1.5 m. (Use the following as necessary: r and m. Assume SI units. Do not enter units in your ansWers.) (a) What is the magnitude of the gravitational force due to the sphere on a particle of mass m located at a distance of 1.6 m from the center of the sphere? F = N. (b) What if it is 1.4 m from the center of the sphere? F = N. (c) Write a general expression for the magnitude of the gravitational force on the particle at a distancer 1.5 m from the center of the sphere. F = Additional Materials eBook Powers of Ten

A 750-kg satellite is in a circular orbit about Earth at a height above Earth equal to Earth's mean radius. (a) Find the satellite's orbital speed. 1768.95 × Your response differs from the correct answer by more than 10%. Double check your calculations. m/s (b) Find the period of its revolution. 12.576 Your response differs from the correct answer by more than 100%. h (c) Find the gravitational force acting on it. 114.11 × Your response differs significantly from the correct answer. Rework your solution from the beginning and check each step carefully. N