The path of one projectile as seen by an observer on another projectile is a/an:

Options

A. straight line
B. parabola
C. ellipse
D. circle

Explanation

To solve the question, "The path of one projectile as seen by an observer on another projectile is a/an:", we need to analyze the motion of two projectiles and how one appears to the other.

### Step-by-Step Solution:

1. **Understanding Projectile Motion**:
- A projectile is an object that is thrown into the air with an initial velocity and follows a curved path under the influence of gravity. The path is typically a parabola when viewed from a stationary point.

2. **Relative Motion**:
- When we consider the motion of one projectile as seen by an observer on another projectile, we are dealing with relative motion. The observer is also in projectile motion, which affects how they perceive the motion of the other projectile.

3. **Setting Up the Problem**:
- Let’s assume we have two projectiles:
- Projectile A (the one being observed) with initial velocity \( u_1 \) at an angle \( \theta_1 \).
- Projectile B (the observer) with initial velocity \( u_2 \) at an angle \( \theta_2 \).

4. **Displacement of Each Projectile**:
- The horizontal and vertical displacements of Projectile A at time \( t \) can be expressed as:
- \( x_A = u_1 \cos(\theta_1) t \)
- \( y_A = u_1 \sin(\theta_1) t - \frac{1}{2} g t^2 \)
- The horizontal and vertical displacements of Projectile B at the same time \( t \) can be expressed as:
- \( x_B = u_2 \cos(\theta_2) t \)
- \( y_B = u_2 \sin(\theta_2) t - \frac{1}{2} g t^2 \)

5. **Relative Displacement**:
- The relative displacement of Projectile A with respect to Projectile B can be defined as:
- \( X = x_A - x_B = (u_1 \cos(\theta_1) - u_2 \cos(\theta_2)) t \)
- \( Y = y_A - y_B = (u_1 \sin(\theta_1) - u_2 \sin(\theta_2)) t \)

6. **Eliminating Time**:
- To find the path of Projectile A as seen by the observer on Projectile B, we can eliminate \( t \) from the equations of \( X \) and \( Y \):
- From \( X \), we can express \( t \) as:
\[ t = \frac{X}{u_1 \cos(\theta_1) - u_2 \cos(\theta_2)} \]
- Substituting this into the equation for \( Y \):
\[ Y = (u_1 \sin(\theta_1) - u_2 \sin(\theta_2)) \left(\frac{X}{u_1 \cos(\theta_1) - u_2 \cos(\theta_2)}\right) \]

7. **Linear Relationship**:
- The resulting equation can be simplified to show that \( Y \) is directly proportional to \( X \):
\[ Y = mX \]
- This indicates that the path of Projectile A as seen by the observer on Projectile B is a straight line.

8. **Conclusion**:
- Therefore, the path of one projectile as seen by an observer on another projectile is a **straight line**.