The driver of a car moving towards a rocket launching with a speed of 6 `ms^(-1)` observed that the rocket is moving with speed of 10 `ms^(-1)` The upward speed of the rocket as seen by the stationary observer is nearly

Options

A. `4 ms^(-1)`
B. `6 ms^(-1)`
C. `8 ms^(-1)`
D. `11 ms^(-1)`

Answer

To solve the problem, we need to find the upward speed of the rocket as seen by a stationary observer, given the speed of the car and the speed of the rocket as observed by the driver in the car.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- Speed of the car (Vc) = 6 m/s (moving towards the rocket)
- Speed of the rocket as observed by the driver in the car (Vrc) = 10 m/s (upward)

2. **Understand the Vector Relationship:**
- The rocket is moving upwards with some speed (Vr) which we need to find.
- The car is moving towards the rocket, which means we can visualize this as a right triangle where:
- One leg represents the upward speed of the rocket (Vr).
- The other leg represents the speed of the car (Vc).
- The hypotenuse represents the speed of the rocket as observed from the car (Vrc).

3. **Apply the Pythagorean Theorem:**
- According to the Pythagorean theorem, we can write:
\[ Vrc^2 = Vr^2 + Vc^2 \]
- Substituting the known values:
\[ 10^2 = Vr^2 + 6^2 \]

4. **Calculate the Squares:**
- Calculate \(10^2\) and \(6^2\):
\[ 100 = Vr^2 + 36 \]

5. **Rearrange the Equation:**
- To find \(Vr^2\), rearrange the equation:
\[ Vr^2 = 100 - 36 \]
\[ Vr^2 = 64 \]

6. **Find the Upward Speed of the Rocket:**
- Taking the square root of both sides:
\[ Vr = \sqrt{64} = 8 \text{ m/s} \]

7. **Conclusion:**
- The upward speed of the rocket as seen by a stationary observer is **8 m/s**.

### Final Answer:
The upward speed of the rocket as seen by a stationary observer is **8 m/s**.