A ball is thrown vertically upwards in air. If the air resistance can not be neglected (Assume it be directly proportionalto velocity) thenthe acceleration of the ball at the highest point will be :

Options

A. 0
B. g
C. `gt g`
D. `lt g`

Answer

To solve the problem, we need to analyze the forces acting on the ball when it reaches the highest point of its trajectory.

### Step-by-Step Solution:

1. **Understanding the Motion**: When a ball is thrown vertically upwards, it moves against the force of gravity until it reaches its highest point. At this point, the ball momentarily stops before it starts to fall back down.

2. **Velocity at the Highest Point**: At the highest point of its trajectory, the velocity of the ball is zero. This is a key point because the air resistance is directly proportional to the velocity of the ball.

3. **Air Resistance**: Since the air resistance is proportional to the velocity, when the velocity is zero (as it is at the highest point), the air resistance also becomes zero.

4. **Forces Acting on the Ball**: At the highest point, the only force acting on the ball is the force of gravity, which acts downwards. The air resistance does not contribute to the net force since it is zero.

5. **Calculating Acceleration**: The acceleration of the ball at the highest point is determined solely by the gravitational force acting on it. The acceleration due to gravity (g) is approximately \(9.81 \, \text{m/s}^2\) downwards.

6. **Conclusion**: Therefore, at the highest point, the acceleration of the ball is equal to the acceleration due to gravity, which is \(g\).

### Final Answer:
The acceleration of the ball at the highest point is \(g\) (approximately \(9.81 \, \text{m/s}^2\) downwards).

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