As part of a daring rescue attempt, the Millennium Eagle coasts between a pair o
ID: 1262950 • Letter: A
Question
As part of a daring rescue attempt, the Millennium Eagle coasts between a pair of twin asteroids, as shown in the figure below where d1 = 2.57 km and d2 = 1.29 km. The mass of the spaceship is 2.57 ? 107 kg and the mass of each asteroid is 3.15 ? 1011 kg. If the Millennium Eagle is at rest at point A what is its speed at point B?
m/s
Explanation / Answer
in the given problem we can see that the speedat B is determined by its kinetic energy at B, which equals thepotential
energy lost
the potential energy at a point is twice thepotential energy due to a single asteroid
so we can write that
(1 / 2) m v2 = - 2 ?U
= - 2 [- G (M m / rB) - (- G (M m / rA))]
= 2 G M m [(1 /rB) - (1 / rA)]
the speed at B will be
v = ?{4 G M [(1 / rB) - (1 /rA)]}
= ?{4 (6.67 x10-11 N . m2 / kg2) (3.15 x1011 kg) [(1 / 1290 m) - (1 / ?((1290m)2 + (2570 m)2))]}
= 0.1895 m / s
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