Final answer:
The initial speed, u, of the dust speck before it collided with the ice cube can be found using the conservation of momentum principle. Since the collision is inelastic, the equation m_dust x u + M_ice x 0 = (m_dust + M_ice) x v allows us to solve for u, resulting in an initial speed of 3000 m/s.
Step-by-step explanation:
The subject of this question is Physics, specifically the principle of conservation of momentum. In a horizontal, frictionless scenario, the total momentum before and after a collision is the same. The dust speck and the ice cube make an inelastic collision, where the dust speck sticks to the ice cube. We can use the formula for conservation of momentum, pinitial = pfinal, to solve for the initial speed of the dust speck.
Let's assign masses and velocities as follows: mdust = 1 ng (which is 1 x 10-9 kg), Mice = 1 g (which is 1 x 10-3 kg), initial speed of the dust speck - u, and final speed of the ice cube post-collision - v = 3 m/s.
The conservation of momentum states that:
mdust × u + Mice × 0 = (mdust + Mice) × v.
Plug in the given values:
1 x 10-9 kg × u + 1 x 10-3 kg × 0 = (1 x 10-9 kg + 1 x 10-3 kg) × 3 m/s.
The mass of the ice cube dominates the equation, simplifying to:
u = (1 x 10-3 kg × 3 m/s) / 1 x 10-9 kg.
Solving this gives us the initial speed of the dust speck u as 3000 m/s.