A bullet is fired from a gun eith a speed of 1000m/s on order to hit target 100 m away At what height above target should the gun be aimed ? (The resistance of air is negligible and g = 10 `m//s^(2)`)

Options

A. 5cm
B. 10cm
C. 15cm
D. 20cm

Answer

To solve the problem, we need to determine the height above the target at which the gun should be aimed in order for the bullet to hit the target 100 meters away. We will follow these steps:

### Step 1: Determine the time taken for the bullet to reach the target.
The time \( t \) taken for the bullet to reach the target can be calculated using the formula:

\[ t = \frac{d}{v} \]

where:
- \( d = 100 \, \text{m} \) (distance to the target)
- \( v = 1000 \, \text{m/s} \) (speed of the bullet)

Substituting the values:

\[ t = \frac{100 \, \text{m}}{1000 \, \text{m/s}} = 0.1 \, \text{s} \]

### Step 2: Calculate the vertical distance fallen due to gravity during this time.
The vertical distance \( h \) that the bullet falls due to gravity can be calculated using the formula:

\[ h = ut + \frac{1}{2}gt^2 \]

where:
- \( u = 0 \, \text{m/s} \) (initial vertical velocity, as the bullet is fired horizontally)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)
- \( t = 0.1 \, \text{s} \)

Substituting the values:

\[ h = 0 \cdot 0.1 + \frac{1}{2} \cdot 10 \cdot (0.1)^2 \]

Calculating \( h \):

\[ h = 0 + \frac{1}{2} \cdot 10 \cdot 0.01 = 0.05 \, \text{m} \]

### Step 3: Convert the height from meters to centimeters.
To express the height in centimeters:

\[ h = 0.05 \, \text{m} = 5 \, \text{cm} \]

### Conclusion
The gun should be aimed at a height of **5 cm** above the target to ensure that the bullet hits the target.

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