Solution 5: Explosion in Orbit
1. Conservation of Momentum:
Mass ratio 1:4. Let $m$ and $4m$. Total $5m$. \[ 5m v_0 = m(-v_0) + 4m v’ \] \[ 5v_0 = -v_0 + 4v’ \implies 4v’ = 6v_0 \implies v’ = 1.5 v_0 \]
Mass ratio 1:4. Let $m$ and $4m$. Total $5m$. \[ 5m v_0 = m(-v_0) + 4m v’ \] \[ 5v_0 = -v_0 + 4v’ \implies 4v’ = 6v_0 \implies v’ = 1.5 v_0 \]
2. Escape Check:
Escape velocity $v_e = \sqrt{2} v_0 \approx 1.414 v_0$. Since $v’ (1.5 v_0) > v_e (1.414 v_0)$, the heavier fragment escapes.
Escape velocity $v_e = \sqrt{2} v_0 \approx 1.414 v_0$. Since $v’ (1.5 v_0) > v_e (1.414 v_0)$, the heavier fragment escapes.
Answer: (d) Escape from the gravitational interaction.