Question

Asteroid Danger (C4M.5): An a teroid is spot- ted moving straight towards a stationary spaceship. The astronauts fire a missile at the asteroid, break- ing it into two pieces, one 2.4 times bigger than the other. The two pieces pass by the spaceship at the same time. If the lighter chunk passes 1800 m from the edge of the 2.2-km-wide ship, will the other chunk hit or miss the spaceship?

Answer 1

The missile while breaking the pieces has given them a horizontal push in addition to the one they already have in the vertical direction.

So the center of mass will keep moving in the same path towards the center of the ship.

The smaller chunk m_Lighter passes the ship from the ship’s edge at 1800 m

So

The smaller chunk passes the ship from the ship’s center d_lighter= 1800 + (ship’s length/2) = 1800 + ( 2.2 x 10³ / 2) = 2900 m

For a two particle system with masses m_Lighter and m_heavier

d_heavier/d_lighter = m_lighter / m_heavier

d_heavier/d_lighter = m_lighter / 2.4m_lighter

d_heavier = d_lighter/2.4

d_heavier = 2900/2.4

d_heavier = 1208.3 m

If the heaver chunk moves from the center of the ship at 1208.3 m

Then it will move from the edge of the ship at the distance d = 1208.3 - 1100 = 108.3 m

This proves that the heavier chunk will miss the spaceship by a distance of 108.3 m