A 75 kg great dane rushes (4m/s) at his much smaller (15kg) beagle friend. After the dogs collide both dogs are stationary. How fast, and in what direction was the beagle running before the collision?

Answer 1

To solve the problem, we can use the principle of conservation of momentum. The total momentum before the collision must be equal to the total momentum after the collision.

1. Define the variables:

   • Mass of the Great Dane (\(m_1\)) = 75 kg
   • Velocity of the Great Dane (\(v_1\)) = 4 m/s
   • Mass of the Beagle (\(m_2\)) = 15 kg
   • Velocity of the Beagle before the collision (\(v_2\)) = ?
   • After the collision, both dogs are stationary, so their final velocities (\(v_f\)) = 0 m/s.

2. Set up the momentum equation: The total momentum before the collision can be expressed as: \[ \text{Total momentum before} = m_1 \cdot v_1 + m_2 \cdot v_2 \]

   The total momentum after the collision is: \[ \text{Total momentum after} = (m_1 + m_2) \cdot 0 = 0 \]

   Thus, we have the equation: \[ m_1 \cdot v_1 + m_2 \cdot v_2 = 0 \]

3. Substitute the known values: \[ (75 , \text{kg}) \cdot (4 , \text{m/s}) + (15 , \text{kg}) \cdot v_2 = 0 \]

4. Calculate the values: \[ 300 , \text{kg m/s} + 15 , \text{kg} \cdot v_2 = 0 \] \[ 15 , \text{kg} \cdot v_2 = -300 , \text{kg m/s} \] \[ v_2 = \frac{-300 , \text{kg m/s}}{15 , \text{kg}} = -20 , \text{m/s} \]

5. Interpret the result: The negative sign indicates that the beagle was running in the opposite direction to the Great Dane. Thus, before the collision, the beagle was running at a speed of 20 m/s in the direction opposite to that of the Great Dane.

Final Answer: The beagle was running at 20 m/s in the opposite direction to the Great Dane.