The time of flight of projectile on an upward inclined plane depends upon.

Options

A. angle of projection
B. angle of inclination of the plane
C. air resistance
D. a and b both

Answer

To determine the factors that affect the time of flight of a projectile on an upward inclined plane, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Problem**:
We have a projectile launched at an angle \( \phi \) from an inclined plane that has an angle of inclination \( \theta \). We need to find out how the time of flight depends on the angle of projection \( \phi \) and the angle of inclination \( \theta \).

2. **Setting Up the Coordinate System**:
We will set up a coordinate system where the x-axis is along the incline and the y-axis is perpendicular to the incline. This simplifies our calculations.

3. **Breaking Down the Initial Velocity**:
The initial velocity \( u \) of the projectile can be broken down into its components:
- The component along the incline (x-direction):
\[ u_x = u \cos \phi \]
- The component perpendicular to the incline (y-direction):
\[ u_y = u \sin \phi \]

4. **Identifying the Effect of Gravity**:
The acceleration due to gravity \( g \) acts downwards. We need to find its components along the inclined plane:
- The component of gravity acting down the incline (x-direction):
\[ g_x = g \sin \theta \]
- The component of gravity acting perpendicular to the incline (y-direction):
\[ g_y = g \cos \theta \]

5. **Using the Time of Flight Formula**:
The time of flight \( T \) for a projectile is given by the formula:
\[ T = \frac{2 u_y}{g_y} \]
Substituting our values for \( u_y \) and \( g_y \):
\[ T = \frac{2 (u \sin \phi)}{g \cos \theta} \]

6. **Analyzing the Result**:
From the equation \( T = \frac{2 u \sin \phi}{g \cos \theta} \), we can see that:
- The time of flight \( T \) is directly proportional to \( \sin \phi \) (angle of projection).
- The time of flight \( T \) is inversely proportional to \( \cos \theta \) (angle of inclination).

7. **Conclusion**:
Therefore, the time of flight of a projectile on an upward inclined plane depends on both the angle of projection \( \phi \) and the angle of inclination \( \theta \).

### Final Answer:
The time of flight of a projectile on an upward inclined plane depends on both the angle of projection \( \phi \) and the angle of inclination \( \theta \).