A fighter jet is launched from an aircraft carrier with the aid of its own engines and a steam-powered catapult. The thrust of its engines is `2.3xx10^(5)N`. In being launched from rest position, it moves through a distance of 87 m and has a kinetic energy of `4.5xx10^(7)` J at lift-off. What is the work done on the jet by the catapult ?

Options

A. `2.0xx10^(6)J`
B. `2.5xx10^(7)J`
C. `6.0xx10^(6)J`
D. `6.5xx10^(7)J`

Answer

To solve the problem, we need to find the work done on the fighter jet by the catapult. We will use the work-energy theorem and the information provided in the question.

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Thrust of the engines, \( F_{\text{engine}} = 2.3 \times 10^5 \, \text{N} \)
- Distance moved, \( d = 87 \, \text{m} \)
- Kinetic energy at lift-off, \( KE = 4.5 \times 10^7 \, \text{J} \)
- Initial kinetic energy, \( KE_{\text{initial}} = 0 \, \text{J} \) (since it starts from rest)

2. **Calculate the Work Done by the Engine:**
- The work done by the engine can be calculated using the formula:
\[ W_{\text{engine}} = F_{\text{engine}} \times d \]
- Substituting the values:
\[ W_{\text{engine}} = (2.3 \times 10^5 \, \text{N}) \times (87 \, \text{m}) = 2.001 \times 10^7 \, \text{J} \]

3. **Apply the Work-Energy Theorem:**
- According to the work-energy theorem, the net work done on the jet is equal to the change in kinetic energy:
\[ W_{\text{net}} = KE_{\text{final}} - KE_{\text{initial}} \]
- Since \( KE_{\text{initial}} = 0 \):
\[ W_{\text{net}} = KE_{\text{final}} - 0 = KE_{\text{final}} = 4.5 \times 10^7 \, \text{J} \]

4. **Express the Net Work Done:**
- The net work done on the jet is the sum of the work done by the engine and the work done by the catapult:
\[ W_{\text{net}} = W_{\text{engine}} + W_{\text{catapult}} \]
- Rearranging gives us:
\[ W_{\text{catapult}} = W_{\text{net}} - W_{\text{engine}} \]

5. **Calculate the Work Done by the Catapult:**
- Substitute the values:
\[ W_{\text{catapult}} = (4.5 \times 10^7 \, \text{J}) - (2.001 \times 10^7 \, \text{J}) = 2.499 \times 10^7 \, \text{J} \]
- Rounding gives:
\[ W_{\text{catapult}} \approx 2.5 \times 10^7 \, \text{J} \]

### Final Answer:
The work done on the jet by the catapult is approximately \( 2.5 \times 10^7 \, \text{J} \).