To find the momentum of each object, we'll use the formula for momentum:
[tex]\[ p = m \times v \][/tex]
where:
- [tex]\( p \)[/tex] is the momentum,
- [tex]\( m \)[/tex] is the mass, and
- [tex]\( v \)[/tex] is the velocity.
### For the Elephant:
The mass of the elephant is [tex]\( 2100 \, \text{kg} \)[/tex] and the velocity is [tex]\( 6.25 \, \text{m/s} \)[/tex].
[tex]\[ p_e = 2100 \, \text{kg} \times 6.25 \, \text{m/s} \][/tex]
[tex]\[ p_e = 13125 \, \text{kg} \cdot \text{m/s} \][/tex]
Thus, the momentum of the elephant is:
[tex]\[ p_e = 13125 \, \text{kg} \cdot \text{m/s} \][/tex]
### For the Tranquilizer Dart:
The mass of the tranquilizer dart is [tex]\( 0.0250 \, \text{kg} \)[/tex] and the velocity is [tex]\( 550 \, \text{m/s} \)[/tex].
[tex]\[ p_d = 0.0250 \, \text{kg} \times 550 \, \text{m/s} \][/tex]
[tex]\[ p_d = 13.75 \, \text{kg} \cdot \text{m/s} \][/tex]
Thus, the momentum of the tranquilizer dart is:
[tex]\[ p_d = 13.75 \, \text{kg} \cdot \text{m/s} \][/tex]
### For the Hunter:
The mass of the hunter is [tex]\( 85.0 \, \text{kg} \)[/tex] and the velocity is [tex]\( 5.45 \, \text{m/s} \)[/tex].
[tex]\[ p_h = 85.0 \, \text{kg} \times 5.45 \, \text{m/s} \][/tex]
[tex]\[ p_h = 463.25 \, \text{kg} \cdot \text{m/s} \][/tex]
Thus, the momentum of the hunter is:
[tex]\[ p_h = 463.25 \, \text{kg} \cdot \text{m/s} \][/tex]
So, the answers are:
1. The momentum of the elephant:
[tex]\[ p_e = 13125 \, \text{kg} \cdot \text{m/s} \][/tex]
2. The momentum of the tranquilizer dart:
[tex]\[ p_d = 13.75 \, \text{kg} \cdot \text{m/s} \][/tex]
3. The momentum of the hunter:
[tex]\[ p_h = 463.25 \, \text{kg} \cdot \text{m/s} \][/tex]
