For body thrown horizontally from the top of a tower,

Options

A. the time of flight depends both on h and v
B. the horizontal Range depends only on v but not on h
C. the time of flight and horizontal Range depend on h but not on v
D. the horizontal Range depends on both v and h

Answer

To solve the problem regarding the motion of a body thrown horizontally from the top of a tower, we need to analyze the time of flight and the horizontal range of the projectile. Here's a step-by-step solution:

### Step 1: Understand the Problem
A body is thrown horizontally from a height (H) with an initial horizontal velocity (B). We need to determine how the time of flight and horizontal range depend on H and B.

### Step 2: Determine Time of Flight
The time of flight (T) for a projectile thrown horizontally is determined by the height from which it is thrown. The formula for the time of flight when an object falls freely under gravity is given by:

\[ T = \sqrt{\frac{2H}{g}} \]

where:
- \( H \) = height of the tower
- \( g \) = acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \))

### Step 3: Calculate Horizontal Range
The horizontal range (R) of the projectile can be calculated using the formula:

\[ R = B \cdot T \]

Substituting the expression for time of flight (T) into the range formula, we get:

\[ R = B \cdot \sqrt{\frac{2H}{g}} \]

### Step 4: Analyze the Dependencies
From the equations derived:
- The time of flight \( T \) depends only on the height \( H \) and does not depend on the horizontal velocity \( B \).
- The horizontal range \( R \) depends on both the horizontal velocity \( B \) and the height \( H \).

### Conclusion
Based on the analysis:
1. **Time of Flight** depends only on \( H \).
2. **Horizontal Range** depends on both \( B \) and \( H \).

Thus, the correct option is that the horizontal range depends on both \( B \) and \( H\).

### Final Answer
The correct option is that the horizontal range depends on both \( B \) and \( H \).

---