To solve the problem, we can use the law of conservation of momentum, which states that in the absence of external forces, the total momentum of a closed system remains constant.
Let's denote:
- \( m_s \) = mass of the spacecraft = 1,000 kg
- \( v_s \) = velocity of the spacecraft = 250 m/s
- \( m_a \) = mass of the asteroid (unknown)
- \( v_a \) = velocity of the asteroid = -25 m/s (negative since it’s moving in the opposite direction)
According to the conservation of momentum:
\[ m_s \cdot v_s + m_a \cdot v_a = 0 \]
Substituting the known values into the equation:
\[ 1000 , \text{kg} \cdot 250 , \text{m/s} + m_a \cdot (-25 , \text{m/s}) = 0 \]
Calculating the momentum of the spacecraft:
\[ 1000 \cdot 250 = 250000 , \text{kg m/s} \]
So the equation becomes:
\[ 250000 - 25m_a = 0 \]
Rearranging the equation to solve for \( m_a \):
\[ 25m_a = 250000 \]
\[ m_a = \frac{250000}{25} = 10000 , \text{kg} \]
The mass of the asteroid is 10,000 kg.
1 answer