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 = 2.97 km and d2 = 1.49 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
To find the speed of the Millennium Eagle at point B, we can use the principle of conservation of momentum. The total momentum before the encounter must be equal to the total momentum after the encounter.
Let's denote the initial velocity of the Millennium Eagle as v1, and the final velocity as v2. Since the mass of the asteroids is much larger than the mass of the spaceship, we can neglect any change in their velocities during the encounter. Therefore, their momentum before and after the encounter is nearly zero.
The initial momentum of the spaceship is given by m1 * v1, and the final momentum is m1 * v2. Applying the conservation of momentum principle, we have:
m1 * v1 = m1 * v2
Since the mass of the spaceship, m1, cancels out, we can simplify the equation to:
v1 = v2
So, the speed of the Millennium Eagle at point B is equal to its initial speed at point A. Therefore, its speed at point B is the same as its initial speed, which is 0 m/s (since it's at rest).
Therefore, the speed of the Millennium Eagle at point B is 0 m/s.