Two bullets are fired simultaneously, horizontally but with different speeds from the same horizontal plane. Which 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

Explanation

To solve the problem of which bullet will hit the ground first when fired simultaneously from the same height but with different horizontal speeds, we can follow these steps:

### Step 1: Understand the scenario
We have two bullets fired horizontally from the same height (let's call it height \( h \)). Bullet 1 has a speed \( v_1 \) and Bullet 2 has a speed \( v_2 \).

**Hint:** Remember that the bullets are fired horizontally, meaning their initial vertical velocities are zero.

### Step 2: Analyze the vertical motion
In the vertical direction, both bullets are subject to the force of gravity. The only force acting on them is the gravitational force, which causes them to accelerate downwards at a rate of \( g \) (acceleration due to gravity).

**Hint:** The vertical motion is independent of the horizontal motion.

### Step 3: Determine the time of flight
The time it takes for an object to fall from a height \( h \) under the influence of gravity can be calculated using the formula:
\[ t = \sqrt{\frac{2h}{g}} \]
This formula shows that the time of flight depends only on the height \( h \) and the acceleration due to gravity \( g \).

**Hint:** The time of flight is the same for both bullets since they are dropped from the same height.

### Step 4: Conclusion
Since both bullets are fired simultaneously from the same height and are only influenced by gravity in the vertical direction, they will both hit the ground at the same time, regardless of their horizontal speeds \( v_1 \) and \( v_2 \).

**Hint:** The horizontal speeds do not affect the time taken to fall; they only affect how far away from the starting point the bullets land.

### Final Answer
Both bullets will hit the ground simultaneously.

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