https://file.aiquickdraw.com/mathbot/file/17285204471058mpxhcih.jpg

The problem in the image is about a horizontally launched projectile, specifically asking to determine the initial velocity of a ball thrown horizontally from the top of a 30-meter-high tower, which lands 15 meters away from the base.

Let's break it down:

### Given:
- Height of the tower, \( h = 30 \, \text{m} \)
- Horizontal distance from the base where the ball lands, \( d = 15 \, \text{m} \)
- The ball is thrown horizontally, so the initial vertical velocity \( v_{0y} = 0 \, \text{m/s} \)

### To Find:
The initial horizontal velocity \( v_0 \).

### Step-by-Step Solution:

#### 1. **Vertical Motion:**
For the vertical motion, the only force acting on the ball is gravity. Using the kinematic equation for vertical displacement:

\[
h = \frac{1}{2} g t^2
\]

where:
- \( h = 30 \, \text{m} \) is the vertical displacement,
- \( g = 9.8 \, \text{m/s}^2 \) is the acceleration due to gravity,
- \( t \) is the time of flight.

Solving for \( t \):

\[
t^2 = \frac{2h}{g} = \frac{2 \times 30}{9.8} \approx 6.12
\]

\[
t \approx \sqrt{6.12} \approx 2.47 \, \text{seconds}
\]

#### 2. **Horizontal Motion:**
The horizontal motion is constant velocity since there's no horizontal acceleration. The horizontal distance covered is:

\[
d = v_0 \cdot t
\]

Solving for \( v_0 \):

\[
v_0 = \frac{d}{t} = \frac{15}{2.47} \approx 6.07 \, \text{m/s}
\]

### Final Answer:
The initial horizontal velocity \( v_0 \) of the ball is approximately **6.07 m/s**.

Would you like further details or have any additional questions?

### Related Questions:
1. How would the initial velocity change if the height of the tower were doubled?
2. What is the total time the ball is in the air if it were thrown at a 45° angle instead of horizontally?
3. How does air resistance affect the horizontal distance traveled in such a scenario?
4. Can you derive the equation for the time of flight for an object thrown horizontally?
5. How would the result change if the value of gravitational acceleration were different (e.g., on the Moon)?

### Tip:
For horizontally launched projectiles, the horizontal and vertical motions are independent of each other, meaning you can analyze them separately.

Bola dilemparkan secara horizontal dari atas menara setinggi 30 m dan mendarat 15 m dari pangkalannya. Berapa kecepatan awal bolanya?

Learn how to calculate the initial horizontal velocity of a ball launched from a 30-meter-high tower that lands 15 meters from its base. The problem involves key concepts of kinematics and projectile motion, with detailed step-by-step solutions suitable for Grades 10-12 students.

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