A ball is projected from the top of a tower at an angle `60^(@)` with the vertical. What happens to the vertical component of its velocity?

Options

A. Increases continuously
B. Decreases continuously
C. Remain unchanged
D. Frist decreases and then increases

Explanation

To solve the problem of what happens to the vertical component of the velocity of a ball projected from the top of a tower at an angle of \(60^\circ\) with the vertical, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Initial Conditions**:
- The ball is projected from the top of a tower at an angle of \(60^\circ\) with respect to the vertical. This means that the angle with respect to the horizontal is \(30^\circ\) (since \(90^\circ - 60^\circ = 30^\circ\)).

2. **Breaking Down the Velocity Components**:
- Let the initial velocity of the ball be \(V\). The vertical component of the initial velocity (\(V_y\)) can be calculated using trigonometric functions:
\[ V_y = V \cdot \cos(60^\circ) \]
- Since \(\cos(60^\circ) = \frac{1}{2}\), we have:
\[ V_y = V \cdot \frac{1}{2} = \frac{V}{2} \]

3. **Analyzing the Motion**:
- As the ball moves upward, the vertical component of its velocity will be affected by gravity. The acceleration due to gravity (\(g\)) acts downward, opposing the upward motion of the ball.

4. **Effect of Gravity on Vertical Velocity**:
- The vertical component of the velocity will decrease as the ball rises due to the gravitational pull. The vertical velocity at any time \(t\) can be expressed as:
\[ V_{y}(t) = V_y - g \cdot t \]
- This shows that the vertical component of the velocity decreases over time until it reaches zero at the maximum height.

5. **Conclusion**:
- Therefore, the vertical component of the ball's velocity decreases as it rises due to the effect of gravity acting in the opposite direction to the motion.