To determine which trial's cart has the greatest momentum at the bottom of the ramp, we need to use the formula for momentum, which is defined as:
[tex]\[ \text{Momentum} = \text{Mass} \times \text{Velocity} \][/tex]
Now, let's calculate the momentum for each trial step-by-step:
### Trial 1:
- Mass: 200 kg
- Velocity: 6.5 m/s
[tex]\[
\text{Momentum} = 200 \, \text{kg} \times 6.5 \, \text{m/s} = 1300 \, \text{kg} \cdot \text{m/s}
\][/tex]
### Trial 2:
- Mass: 220 kg
- Velocity: 5.0 m/s
[tex]\[
\text{Momentum} = 220 \, \text{kg} \times 5.0 \, \text{m/s} = 1100 \, \text{kg} \cdot \text{m/s}
\][/tex]
### Trial 3:
- Mass: 240 kg
- Velocity: 6.4 m/s
[tex]\[
\text{Momentum} = 240 \, \text{kg} \times 6.4 \, \text{m/s} = 1536 \, \text{kg} \cdot \text{m/s}
\][/tex]
### Trial 4:
- Mass: 260 kg
- Velocity: 4.8 m/s
[tex]\[
\text{Momentum} = 260 \, \text{kg} \times 4.8 \, \text{m/s} = 1248 \, \text{kg} \cdot \text{m/s}
\][/tex]
Now we compare the momentum values of all four trials:
- Trial 1: 1300 kg·m/s
- Trial 2: 1100 kg·m/s
- Trial 3: 1536 kg·m/s
- Trial 4: 1248 kg·m/s
The trial with the greatest momentum at the bottom of the ramp is Trial 3, with a momentum of 1536 kg·m/s.
Therefore, the correct answer is:
[tex]\[ \text{Trial 3, because this trial has a large mass and a large velocity.} \][/tex]
