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?

Q: density to be 5650kg/m³. (a) What must the muzzle velocity for the projectile to escape the planet's…

A: we are finding Mass first ,then we calculate the part a question :

Q: The escape speed of a projectile on the earth’s surface is 11.2 km s-1. A body is projected out with…

A: Let ve be the escape velocity of the projectile, v be the actual speed of the projectile, v’ be the…

Q: An asteroid of mass 1.1 x 105 kg must be diverted 7.5 hours before striking the earth. How can this…

A: Given,  Mass of asteroid, M = 1.1×1015 kg  Mass of MT bomb , m = 100 MT = 109kg ×100

Q: If Earth orbits the Sun once per 365 days on a circular orbit with radius dEarth 1.5 × 10° km, what…

A: V = 2πdearth / T 365 days = 3.15 × 10⁷ sec

Q: Prove that the total gravitational potential energy can be written as W = .5 ∫d3xρ(x)Φ(x). ρ(x) and…

A: To derive the expression for the total gravitational potential energy, we start with the definition…

Q: In introductory physics laboratories, a typical Cavendish balance for measuring the gravitational…

A: Gravity pulls an object towards it. It is a central force which brings 2 bodies towards each other.…

Q: At apoapsis (furthest point from the star), the

A:

Q: A satellite of mass 175 kg is launched from a site on Earth's equator into an orbit at 195 km above…

A: Solution: Given data: Mass of the satellite, m = 175 kg, Height of the orbit, h = 195 km =1.95×105 m…

Q: Your response differs from the correct answer by more than 10%. Double check your calculations. m…

A:

Q: A ring of radius 6.5 m lies in the x-y plane, centered on the origin. The portions of the ring in…

A:

Q: What will be the escape velocity from the surface of the moon if it is 11.2 km/s at the surface of…

A: The minimum velocity required by anyone or any thing to resist the gravitational pull of the planet…

Q: (a) What is the escape speed on a spherical asteroid whose radius is 106 km and whose gravitational…

A:

Q: escape velocity

A:

Q: tellite travels with constant speed vin a circular orbit 320 km above the earth's surface. Calculate…

A:

Q: The star Sirus A has a mass of 2.06 MO and a radius of 1.71 RO, where M0 is the mass of the Sun…

A:

Q: Q. 37 : What value of speed must be given to a projectile so as to launch it form earth's surface at…

A:

Q: A planet has a mass of M1, a radius of R1, and a density of ρ1. A second planet has a mass of M2, a…

A:

Q: In introductory physics laboratories, a typical Cavendish balance for measuring the gravitational…

A:

Q: A satellite is given a boost of 595 MJ of energy to move it from its initial orbit at an altitude of…

A:

Q: An artificial satellite is in a circular orbit 6.50 × 10² km from the surface of a planet of radius…

A: Given data: The distance between satellite and planet is, d= 6.50×102 km=6.50×105 m The radius of…

Q: A ring of radius 6.5 m lies in the x-y plane, centered on the origin. The portions of the ring in…

A: Given data: Radius of the ring, R=6.5 m Mass density of first and third quadrant of the ring, ρ1=3.6…

Q: Two satellites are in circular equatorial orbits of different altitudes. Satellite A is in a…

A: 1. For an elevation angle of 0 degrees:  Satellite A is in a geosynchronous orbit, meaning it…

Q: Problem 3: A particle with mass m,=2 kg is located at x=0 while a particle with mass m,=128 kg is…

A:

Q: A probe of mass 100 kg is coasting through a dense gas cloud in deep space, where g = 0.  There is…

A: Using Newton’s second law of motion mdvdt=Fdmdvdt=-0.6v∫vivfdvv=∫-0.6mdtlnvfvi=-0.6tm

Q: An asteroid, headed directly toward Earth, has a speed of 12 km/s relative to the planet when the…

A: Solution

Q: (a) What is the escape speed on a spherical asteroid whose radius is 624 km and whose gravitational…

A: Given: The radius of the asteroid is 624 km. The acceleration due to gravity on the surface of the…

Q: (a) What is the escape speed on a spherical asteroid whose radius is 103 km and whose gravitational…

A:

Q: (a) Evaluate the gravitational potential energy (in J) between two 4.00 kg spherical steel balls…

A: The data given is as follows: 1. Mass of the two spherical balls, m1=m2=4 kg 2. Center to center…

Q: NOTE: Your answer suggests that you have assumed constant gravitational

A: Explained as, F=-GMMR+y2

Q: A bullet is fired vertically upwards with velocity v from the surface of a spherical planet. When it…

A: Let h represent the bullet's climb in height.  Gravitational acceleration changes with height as…

Q: Consider an object that is in an elliptical orbit with semimajor axis a = 7.9×106 m about a planet…

A: Relation b/w the apogee ( furthest ) and perigee (closest) point with Semimajor axis(a) are as:…

Q: 1. In the atmosphere of a planet or large satellite the hot molecules or atoms may be moving fast…

A: 1-Average velocity of any one molecule is measured by temperature of gas. But velocity of individual…

Q: (a) What is the escape speed on a spherical asteroid whose radius is 502 km and whose gravitational…

A: radius , R = 502 km = 502 x 103 m gravitational acceleration , ag = 0.87 m/s2  radial speed , v =…

Q: The ratio of the radius of the Earth to that of the Moon is 10. The ratio of acceleration due to…

A:

Q: (a) What is the escape speed on a spherical asteroid whose radius is 685 km and whose gravitational…

A: This problem can be solved using basic formula related to gravitation

Q: A spacecraft is launched from Cape Canaveral to a 28.3 400 km. We want to reach the ISS, which orbit…

A: On an orbital inclination of 51.6 degrees, the station travels from west to east. Depending on the…

Q: What is the escape speed on a spherical asteroid whose radius is 274 km and whose gravitational…

A:

Q: (a) Evaluate the gravitational potential energy (in J) between two 6.00 kg spherical steel balls…

A: Answer:-  (a)  Mass of a ball(m1) = 6.00 kg  Mass of second ball(m2) = 6.00kg  The initial center to…

Q: A piece of spacecraft debris initially at rest falls to the earth’s surface from a height above the…

A: From energy conservation,12m×0+-GMmR+R/2=12mv2+-GMmRG=gravitation constantM=mass of…

Central Force

Central force is the force that acts along the center of mass of one body to the center of mass of another body. Its direction from or away from a point on a body to another is called the center of the force. Such forces include gravitational force between two massive objects or electrostatic forces between two charged particles. So from atoms to planets, the central forces play an important role in shaping our daily lives. One of the remarkable features of central forces is that they are conservative, i.e. the total energy of a central force system can always be expressed as a gradient of a potential energy function.