Let's start by understanding the concept of impulse. Impulse is defined as the product of the force applied to an object and the time duration over which the force is applied. Mathematically:
[tex]\[ \text{Impulse} = \text{Force} \times \text{Time} \][/tex]
For Ball A, we know from the table that:
- The original force applied is [tex]\( 50 \, \text{N} \)[/tex]
- The time duration is [tex]\( 1.25 \, \text{s} \)[/tex]
- The original impulse is calculated as:
[tex]\[ \text{Impulse}_{\text{original}} = 50 \, \text{N} \times 1.25 \, \text{s} = 62.5 \, \text{N} \cdot \text{s} \][/tex]
Now, we are asked to determine what happens to the impulse if the force on Ball A doubles while the time remains the same. If the force doubles, the new force applied will be:
[tex]\[ \text{Force}_{\text{new}} = 2 \times 50 \, \text{N} = 100 \, \text{N} \][/tex]
The time remains the same at [tex]\( 1.25 \, \text{s} \)[/tex]. Thus, the new impulse can be calculated as:
[tex]\[ \text{Impulse}_{\text{new}} = \text{Force}_{\text{new}} \times \text{Time} = 100 \, \text{N} \times 1.25 \, \text{s} = 125.0 \, \text{N} \cdot \text{s} \][/tex]
Comparing the new impulse with the original impulse, we see that:
[tex]\[ \frac{\text{Impulse}_{\text{new}}}{\text{Impulse}_{\text{original}}} = \frac{125.0 \, \text{N} \cdot \text{s}}{62.5 \, \text{N} \cdot \text{s}} = 2 \][/tex]
This means the new impulse is twice the original impulse. Therefore, when the force on Ball A doubles while the time remains the same, the impulse also doubles.
So, the correct answer is:
- It doubles.
