A bullet is fired from a rifle that is held 1.6 m above the ground in a horizontal position. The initial speed of the bullet is 1100 m/s. Find the time it takes for the bullet to strike the ground and the horizontal distance traveled by the bullet.

Options

A. 0.24 s, 693 m
B. 0.57 s, 630 m
C. 0.32 s, 440 m
D. 0.63 s, 352 m

Answer

To solve the problem, we need to break it down into two parts: finding the time it takes for the bullet to strike the ground and then calculating the horizontal distance traveled by the bullet.

### Step 1: Calculate the time to strike the ground

1. **Identify the known values:**
- Height (h) = 1.6 m (the bullet is fired from this height)
- Initial vertical velocity (u) = 0 m/s (the bullet is fired horizontally)
- Acceleration due to gravity (a) = -9.8 m/s² (downward)

2. **Use the second equation of motion:**
The equation we will use is:
\[ h = ut + \frac{1}{2} a t^2 \]
Substituting the known values into the equation:
\[ -1.6 = 0 \cdot t + \frac{1}{2} (-9.8) t^2 \]
This simplifies to:
\[ -1.6 = -4.9 t^2 \]

3. **Solve for t²:**
Rearranging gives:
\[ t^2 = \frac{1.6}{4.9} \]
Calculating this:
\[ t^2 \approx 0.3265 \]

4. **Calculate t:**
Taking the square root:
\[ t \approx \sqrt{0.3265} \approx 0.57 \text{ seconds} \]

### Step 2: Calculate the horizontal distance traveled

1. **Identify the horizontal motion:**
- Initial horizontal velocity (v) = 1100 m/s (the speed of the bullet)
- Time (t) = 0.57 seconds (calculated from Step 1)

2. **Use the formula for horizontal distance:**
The horizontal distance (d) can be calculated using:
\[ d = v \cdot t \]
Substituting the known values:
\[ d = 1100 \cdot 0.57 \]

3. **Calculate d:**
\[ d \approx 627 \text{ meters} \]

### Final Results
- Time to strike the ground: **0.57 seconds**
- Horizontal distance traveled: **627 meters**