To determine which trial has the greatest impulse, we need to use the formula for impulse, which is:
[tex]\[
\text{Impulse} = \text{Force} \times \text{Time}
\][/tex]
Given:
- The force in each trial is [tex]\(500 \, \text{N}\)[/tex].
- The times for each trial are provided.
Let's calculate the impulse for each trial step-by-step:
#### Trial 1:
[tex]\[
\text{Impulse}_1 = 500 \, \text{N} \times 0.25 \, \text{s} = 125 \, \text{Ns}
\][/tex]
#### Trial 2:
[tex]\[
\text{Impulse}_2 = 500 \, \text{N} \times 0.15 \, \text{s} = 75 \, \text{Ns}
\][/tex]
#### Trial 3:
[tex]\[
\text{Impulse}_3 = 500 \, \text{N} \times 0.45 \, \text{s} = 225 \, \text{Ns}
\][/tex]
#### Trial 4:
[tex]\[
\text{Impulse}_4 = 500 \, \text{N} \times 0.33 \, \text{s} = 165 \, \text{Ns}
\][/tex]
Now, let's compare the impulses calculated in each trial:
- [tex]\(\text{Impulse}_1 = 125 \, \text{Ns}\)[/tex]
- [tex]\(\text{Impulse}_2 = 75 \, \text{Ns}\)[/tex]
- [tex]\(\text{Impulse}_3 = 225 \, \text{Ns}\)[/tex]
- [tex]\(\text{Impulse}_4 = 165 \, \text{Ns}\)[/tex]
From these calculations, we see that the greatest impulse is [tex]\(225 \, \text{Ns}\)[/tex] which occurs in Trial 3.
Therefore, the trial with the greatest impulse is:
[tex]\[
\boxed{\text{Trial 3}}
\][/tex]
