A jet airplane travelling at the speed of `450 kmh ^(-1)`ejects the burnt gases at the speed of `1200 kmh^(-1)` relative to the jet airplane. Find the speed of the brunt gases w.r.t a stationary observer on earth .

Answer

To solve the problem of finding the speed of the burnt gases with respect to a stationary observer on Earth, we can follow these steps:

### Step 1: Understand the given information
- The speed of the jet airplane, \( v_{jet} = 450 \, \text{km/h} \) (upward).
- The speed of the burnt gases relative to the jet airplane, \( v_{gases, relative} = 1200 \, \text{km/h} \) (downward).

### Step 2: Define the directions
- We will assume upward direction as positive (along the positive y-axis) and downward direction as negative (along the negative y-axis).
- Therefore, we can represent the speeds as:
- \( v_{jet} = +450 \, \text{km/h} \)
- \( v_{gases, relative} = -1200 \, \text{km/h} \)

### Step 3: Use the relative velocity formula
The velocity of the burnt gases with respect to a stationary observer on Earth can be calculated using the formula:
\[ v_{gases, ground} = v_{gases, relative} + v_{jet} \]

### Step 4: Substitute the values
Substituting the values we have:
\[ v_{gases, ground} = -1200 \, \text{km/h} + 450 \, \text{km/h} \]

### Step 5: Calculate the resultant speed
Now, performing the calculation:
\[ v_{gases, ground} = -1200 + 450 = -750 \, \text{km/h} \]

### Step 6: Interpret the result
The negative sign indicates that the speed of the burnt gases is directed downward. Therefore, the speed of the burnt gases with respect to a stationary observer on Earth is:
\[ \text{Speed of burnt gases} = 750 \, \text{km/h} \, \text{(downward)} \]

### Final Answer
The speed of the burnt gases with respect to a stationary observer on Earth is \( 750 \, \text{km/h} \) downward.

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