A projectile is fired vertically from a planet's surface with an initial speed of 6.5 km/s. Neglect aerodynamic drag and determine how high above the earth it will go in km. Assume the planet radius and mass are 16510 km and 7.7E24 kg, respectively. NOTE: Acceleration due to gravity IS NOT CONSTANT. Derive and express algebraic solution in terms of givens: vo, Rp, Mp and G.
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- Please don't provide handwritten solution .....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.In 2000 , NASA placed a satellite in orbit around an asteroid. consider a spherical asteroid with a mass of 1.50 * 10^16 kg and a radius of 10.0 km what is the speed of a satellitie orbiting 5.90 km above the surface ? express with appropriate units what is the escape speed from the asteroid (express with appropriate units)
- Please solveLet the radius of the Earth be R, and we approximate the Earth as a sphere. In order for an object to glide along the equator of the Earth at sea level, what is the speed at which it needs to be moving? gR gR VgR O (gR)?While we usually assume that the force of gravity is constant, it actually decreases with altitude according to the formula Frau = mgre • where ro is the radius of Earth, and r is the distance from the Earth's center. a) Why can we approximate the force of gravity as constant at the surface of Earth? b) Show that a(r)dr = vdv. c) If the particle is fired vertically with velocity vo from Earth's surface, determine its velocity as a function of position r. (Hint: use the result of part b
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