Energy of a Spacecraft Part A Very far from earth (at R 00), a spacecraft has ru

Question

Energy of a Spacecraft Part A Very far from earth (at R 00), a spacecraft has run out of fuel and its kinetic energy is zero. If only the gravitational force of the earth were to act on it (ie, neglect the forces from the sun and other solar system objects), the spacecraft would eventually crash into the earth. The mass of the earth is Me and its radius is Re Neglect air Find the speed se of the spacecraft when it crashes into the earth. Express the speed in terms of Me. R, and the universal gravitational constant G resistance throughout this problem, since the spacecraft is primanly moving through the near vacuum of space 2GM Submit Submit Hints My Answers Give Up Review Part Incorrect: Try Again; 2 attempts remaining

Explanation / Answer

here,

let the speed of aircraft when it strikes earth is v

initial distace , d2 = inifinte

final distance , d1 = Re

Now, Using conservation of energy

change in kinetic energy + change in potential energy = 0

0.5 * m * v^2 - G * Me * m * (1/Re -1/infinite)

0.5 * v^2 = G * Me/Re

V = sqrt(2*G*Me/Re)

the speed of the spacecraft is sqrt(2*G*Me/Re)

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