Two bullets are fired simultaneously, horizontally and with different speeds from the same place. Whch bullet will hit the ground first?

Options

A. the faster one
B. the slower one
C. both will reach simultaneously
D. depends on the masses

Answer

To determine which bullet will hit the ground first when two bullets are fired horizontally with different speeds, we can analyze the situation step by step.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We have two bullets fired horizontally from the same height.
- They have different horizontal speeds (let's call them \( v_1 \) and \( v_2 \)).
- We need to find out which bullet will hit the ground first.

2. **Identifying the Forces**:
- Both bullets are subject to the same gravitational force acting downwards.
- The only force acting on them in the vertical direction is gravity.

3. **Vertical Motion Analysis**:
- Since both bullets are fired horizontally, their initial vertical velocity (\( u_y \)) is 0.
- The time taken to hit the ground (time of flight) depends solely on the vertical motion, which is influenced by gravity.

4. **Time of Flight Formula**:
- The time of flight for an object in free fall can be given by the formula:
\[ t = \sqrt{\frac{2h}{g}} \]
where \( h \) is the height from which the bullets are fired and \( g \) is the acceleration due to gravity.
- Since both bullets are fired from the same height and are under the influence of the same gravitational acceleration, the time of flight will be the same for both.

5. **Conclusion**:
- Regardless of their horizontal speeds, both bullets will hit the ground at the same time because their vertical motion is independent of their horizontal motion.
- Therefore, both bullets will hit the ground simultaneously.

### Final Answer:
Both bullets will hit the ground at the same time.