A rugby player with a mass of 60.0 kg is running to the right at a speed of 5.50 m/s toward another player of mass 94.0 kg, who is running in the opposite direction at a speed of 5.20 m/s. What is the total momentum of the two players? (Assume the positive direction is to the right. Indicate the direction with the sign of your answer.)
The correct answer and explanation is:
To calculate the total momentum of the two rugby players, we need to use the formula for momentum, which is: p=m×vp = m \times v
Where:
- pp is momentum,
- mm is mass,
- vv is velocity.
Step 1: Calculate the momentum of the first player
The first player has a mass of 60.0 kg and is moving to the right with a speed of 5.50 m/s. Since the direction to the right is considered positive, we have: p1=(60.0 kg)×(5.50 m/s)=330.0 kg⋅m/sp_1 = (60.0 \, \text{kg}) \times (5.50 \, \text{m/s}) = 330.0 \, \text{kg} \cdot \text{m/s}
Step 2: Calculate the momentum of the second player
The second player has a mass of 94.0 kg and is moving in the opposite direction (to the left) at 5.20 m/s. Since this player is moving in the opposite direction, we assign a negative sign to the velocity. Therefore: p2=(94.0 kg)×(−5.20 m/s)=−488.8 kg⋅m/sp_2 = (94.0 \, \text{kg}) \times (-5.20 \, \text{m/s}) = -488.8 \, \text{kg} \cdot \text{m/s}
Step 3: Find the total momentum
The total momentum is the sum of the momenta of both players: ptotal=p1+p2=330.0 kg⋅m/s+(−488.8 kg⋅m/s)p_{\text{total}} = p_1 + p_2 = 330.0 \, \text{kg} \cdot \text{m/s} + (-488.8 \, \text{kg} \cdot \text{m/s}) ptotal=−158.8 kg⋅m/sp_{\text{total}} = -158.8 \, \text{kg} \cdot \text{m/s}
Explanation:
The total momentum of the two players is -158.8 kg·m/s, which means that the total momentum is directed to the left (negative direction). This result occurs because the second player (with a greater mass) is moving faster in the opposite direction, so their momentum “overpowers” that of the first player. This negative value indicates that the overall motion of the system is towards the left.