To solve this problem, we can use the principle of levers, which states that \( \text{Force} \times \text{Distance} = \text{Resistance} \times \text{Resistance Distance} \).
Here, we know the following:
- Resistance (the weight of the tree) is \( 960 \) N.
- Distance (the height we want to raise it) is \( 45 \) cm (which equals \( 0.45 \) meters).
- The distance you press down the lever is \( 2 \) meters.
Using the formula:
\[ F \times d = R \times r \]
Where:
- \( F \) = force applied (what we are trying to find)
- \( d \) = distance moved by applied force (2 m)
- \( R \) = load/weight (960 N)
- \( r \) = distance moved by the load (0.45 m)
Now, we can rearrange this equation to solve for \( F \):
\[ F = \frac{R \times r}{d} \]
Substituting in the values:
\[ F = \frac{960 , \text{N} \times 0.45 , \text{m}}{2 , \text{m}} \]
Calculating this:
\[ F = \frac{432 , \text{N}}{2} = 216 , \text{N} \]
So, the force the gardeners would use to lift the tree using the lever is \( 216 , \text{N} \).
Therefore, the correct response is 216 N.