At the beginning of a basketball game, a referee tosses the ball straight up with a speed of 4.6 m/s. A player cannot touch the ball until after it reaches its maximum height and begains to fall down. What is the minimum time that a player must wait before touching the ball ?

Options

A. 0.24 s
B. 0.66 s
C. 0.47 s
D. 0.94 s

Answer

To solve the problem, we need to determine the time it takes for the basketball to reach its maximum height after being tossed straight up by the referee. This is the minimum time the player must wait before they can touch the ball.

### Step-by-Step Solution:

1. **Identify Given Values**:
- Initial velocity of the ball (u) = 4.6 m/s (upward)
- Acceleration due to gravity (a) = -9.8 m/s² (downward)

2. **Understand the Motion**:
- The ball is thrown upwards, and it will decelerate due to gravity until it reaches its maximum height, where its velocity will be zero.

3. **Use the First Equation of Motion**:
- The first equation of motion is given by:
\[ v = u + at \]
- Here, \(v\) is the final velocity (0 m/s at maximum height), \(u\) is the initial velocity (4.6 m/s), \(a\) is the acceleration (-9.8 m/s²), and \(t\) is the time taken to reach maximum height.

4. **Set Up the Equation**:
- Plugging in the values into the equation:
\[ 0 = 4.6 + (-9.8)t \]

5. **Rearrange the Equation**:
- Rearranging gives:
\[ 9.8t = 4.6 \]

6. **Solve for Time (t)**:
- Divide both sides by 9.8:
\[ t = \frac{4.6}{9.8} \]
- Calculating this gives:
\[ t \approx 0.469 \text{ seconds} \]

7. **Conclusion**:
- Therefore, the minimum time that the player must wait before touching the ball is approximately **0.47 seconds**.