A bullet moving at 20 m/sec. strikes a wooden plank and penetrates 4 cm before coming to stop. The time taken to stop is

Options

A. 0.08 sec
B. 0.16 sec
C. 0.04 sec
D. 0.004 sec

Answer

To solve the problem of determining the time taken for a bullet moving at 20 m/s to stop after penetrating 4 cm into a wooden plank, we can follow these steps:

### Step 1: Identify the given values
- Initial velocity (u) = 20 m/s
- Final velocity (v) = 0 m/s (since the bullet comes to a stop)
- Distance penetrated (s) = 4 cm = 0.04 m (convert cm to m)

### Step 2: Use the kinematic equation
We can use the kinematic equation:
\[ v^2 = u^2 + 2as \]
Where:
- \( v \) = final velocity
- \( u \) = initial velocity
- \( a \) = acceleration (or deceleration in this case)
- \( s \) = displacement

### Step 3: Substitute the known values into the equation
Substituting the values we have:
\[ 0^2 = (20)^2 + 2a(0.04) \]
This simplifies to:
\[ 0 = 400 + 0.08a \]

### Step 4: Solve for acceleration (a)
Rearranging the equation to solve for \( a \):
\[ 0.08a = -400 \]
\[ a = \frac{-400}{0.08} \]
\[ a = -5000 \, \text{m/s}^2 \]

### Step 5: Use another kinematic equation to find time (t)
Now we can use the equation:
\[ v = u + at \]
Substituting the known values:
\[ 0 = 20 + (-5000)t \]

### Step 6: Rearranging to solve for time (t)
Rearranging gives:
\[ 5000t = 20 \]
\[ t = \frac{20}{5000} \]
\[ t = 0.004 \, \text{seconds} \]

### Conclusion
The time taken for the bullet to stop is **0.004 seconds**.

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