A projectilie is throw horizontally from the top of a tower on the surface of earth. Identify the trajectory which is not possible assuming no air resistance

Options

A. straight line
B. circular
C. ellipticad
D. parabolic

Answer

To solve the problem of identifying the trajectory that is not possible for a projectile thrown horizontally from the top of a tower, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Setup**:
- A projectile is thrown horizontally from the top of a tower.
- The only force acting on the projectile after it is thrown is gravity (assuming no air resistance).

2. **Analyzing the Motion**:
- The motion of the projectile can be separated into two components: horizontal and vertical.
- The horizontal motion is uniform (constant velocity), while the vertical motion is uniformly accelerated (due to gravity).

3. **Equations of Motion**:
- For vertical motion, the displacement \( y \) can be described by the equation:
\[ y = \frac{1}{2} g t^2 \]
- For horizontal motion, the displacement \( x \) is given by:
\[ x = v_0 t \]
- Here, \( g \) is the acceleration due to gravity, \( v_0 \) is the initial horizontal velocity, and \( t \) is the time of flight.

4. **Eliminating Time**:
- From the horizontal motion equation, we can express time \( t \) as:
\[ t = \frac{x}{v_0} \]
- Substituting this into the vertical motion equation gives:
\[ y = \frac{1}{2} g \left(\frac{x}{v_0}\right)^2 \]
- This simplifies to:
\[ y = \frac{g}{2v_0^2} x^2 \]
- This equation represents a parabolic trajectory.

5. **Identifying Possible Trajectories**:
- Since the trajectory derived from the equations of motion is parabolic, any trajectory that is not parabolic cannot be achieved by the projectile.
- Therefore, we need to identify which of the given options (if any) do not represent a parabolic path.

6. **Conclusion**:
- The only trajectory that is not possible for a projectile thrown horizontally from a height (assuming no air resistance) is any trajectory that is not parabolic.
- Thus, the answer will be any option that does not represent a parabola.