Planet Zero has a mass of 4.0 F*10²³ kg and a radius of 2.0 *10⁶ m.A 10-kg space probe is launched vertically from the surface of Zero with an initial kinetic energy of 8.0 *10⁷ J.What maximum distance from the center of Zero is achieved by the probe? A)3.2 * 10⁶ m B)4.0 * 10⁶ m C)6.0 *10⁶ m D)5.0 * 10⁶ m E)2.5 *10⁶ m

Question

Quizplus · Accepted Answer

We can use the conservation of energy to find the maximum distance from the center of Zero. At the surface of Zero, the probe has kinetic energy of 8.0e17 J and potential energy of -GMm/R, where M is the mass of Zero, m is the mass of the probe, R is the radius of Zero, and G is the gravitational constant. At the maximum distance d from the center of Zero, the probe has potential energy of -GMm/(R+d) and kinetic energy of 0. Setting these two energies equal, we have:

8.0e17 J = -GMm/R - (-GMm/(R+d))
8.0e17 J = GMm(R+d)/(R(R+d))
d = R(8.0e17/GMm - 1)

Plugging in the given values for M, R, m, and the kinetic energy, we get:

d = 2.0e16 m *(8.0e17 J / (6.6743e-11 N(m/kg)^2*(4.0e10 kg)*(10 kg)) - 1)
d = 5.0e16 m
Therefore, the maximum distance from the center of Zero is 5.0e16 m or 5.0 × 10^16 m, which is closest to choice D: 5.0e16 m.

Planet Zero Has a Mass of 4