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

Options

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

Explanation

To solve the problem, we need to find the upward speed of the rocket as seen by a stationary observer. We will use the concept of relative velocity and the Pythagorean theorem since the velocities involved are perpendicular to each other.

### 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 (VRC) = 10 m/s

2. **Understand the Directions:**
- The car is moving horizontally towards the rocket.
- The rocket is moving vertically upwards.

3. **Use the Pythagorean Theorem:**
Since the car's velocity and the rocket's upward velocity are perpendicular to each other, we can use the Pythagorean theorem to find the upward speed of the rocket (Vo) as seen by a stationary observer.

The relationship can be expressed as:
\[ VRC^2 = VC^2 + Vo^2 \]

4. **Substitute the Known Values:**
Substitute VC = 6 m/s and VRC = 10 m/s into the equation:
\[ 10^2 = 6^2 + Vo^2 \]
\[ 100 = 36 + Vo^2 \]

5. **Solve for Vo:**
Rearranging the equation to find Vo:
\[ Vo^2 = 100 - 36 \]
\[ Vo^2 = 64 \]
Taking the square root of both sides:
\[ Vo = \sqrt{64} = 8 \text{ m/s} \]

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

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

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