Question

A 3.7-kg falcon catches a 2.5-kg dove from behind in midair. What is their velocity in unit of m/s after impact if the falcon’s velocity is initially 46.6 m/s and the dove’s velocity is 10.8 m/s in the same direction?

Answer 1

The final velocity of the falcon and the dove after impact is 35.92 m/s.

Step-by-step explanation:

In this scenario, we can apply the principle of conservation of linear momentum, which states that the total linear momentum of an isolated system remains constant if no external forces act on it. The equation for conservation of linear momentum is given by:

`\[m_1 \cdot v_(1i) + m_2 \cdot v_(2i) = m_1 \cdot v_(1f) + m_2 \cdot v_(2f)\]`

Where:

`\(m_1\)` and
`\(m_2\)` are the masses of the falcon and dove, respectively.

`\(v_(1i)\)` and
`\(v_(2i)\)` are the initial velocities of the falcon and dove, respectively.

`\(v_(1f)\)` and
`\(v_(2f)\)` are the final velocities of the falcon and dove, respectively.

Substituting the given values into the equation:

`\[ (3.7 \ kg \cdot 46.6 \ m/s) + (2.5 \ kg \cdot 10.8 \ m/s) = (3.7 \ kg \cdot v_(1f)) + (2.5 \ kg \cdot v_(2f)) \]`

Solving for the final velocity
`(\(v_(1f) = v_(2f)\))` gives us the final answer.

After solving, we find that the final velocity
`(\(v_(1f) = v_(2f)\))` is approximately 35.92 m/s.

In summary, the conservation of linear momentum principle allows us to determine the final velocity of both the falcon and the dove after the impact, taking into account their masses and initial velocities.