80m/s while a 15,000 kg truck is traveling at 20m/s Which has the greater momentum? A 300 kg snowmobile is traveling at 30m/s How fast would a 200 kg snowmobile need to travel to have the same momentum?

To determine which has the greater momentum, we use the formula for momentum \( p = mv \), where \( m \) is mass and \( v \) is velocity.<br /><br />For the 300 kg snowmobile traveling at 80 m/s:<br />\[ p = 300 \, \text{kg} \times 80 \, \text{m/s} = 24000 \, \text{kg} \cdot \text{m/s} \]<br /><br />For the 15,000 kg truck traveling at 20 m/s:<br />\[ p = 15000 \, \text{kg} \times 20 \, \text{m/s} = 300000 \, \text{kg} \cdot \text{m/s} \]<br /><br />The truck has the greater momentum.<br /><br />Next, to find how fast a 200 kg snowmobile would need to travel to have the same momentum as the 300 kg snowmobile traveling at 30 m/s:<br /><br />First, calculate the momentum of the 300 kg snowmobile at 30 m/s:<br />\[ p = 300 \, \text{kg} \times 30 \, \text{m/s} = 9000 \, \text{kg} \cdot \text{m/s} \]<br /><br />Now, set this equal to the momentum of the 200 kg snowmobile and solve for its velocity \( v \):<br />\[ 9000 \, \text{kg} \cdot \text{m/s} = 200 \, \text{kg} \times v \]<br />\[ v = \frac{9000 \, \text{kg} \cdot \text{m/s}}{200 \, \text{kg}} = 45 \, \text{m/s} \]<br /><br />So, the 200 kg snowmobile would need to travel at 45 m/s to have the same momentum.