A bullet penetrates 7 cm into a block of wood when fired at a speed of 33 m/s. Find the deceleration and the time taken to stop.
egb
To find the deceleration and the time taken to stop, we need to use the equations of motion. Here's how you can approach it:
Step 1: Identify what is given in the problem:
- Initial speed of the bullet (u) = 33 m/s
- Distance penetrated by the bullet (s) = 7 cm = 0.07 m
- Final speed of the bullet (v) = 0 m/s (stopped)
Step 2: Determine the acceleration (a):
The acceleration can be calculated using the equation of motion:
v^2 = u^2 + 2as
Plugging in the known values:
0^2 = 33^2 + 2a(0.07)
0 = 1089 + 0.14a [simplifying the equation]
Step 3: Solve for the acceleration:
Rearrange the equation to solve for acceleration (a):
0.14a = -1089
a = -1089 / 0.14 ≈ -7785 m/s^2
The negative sign indicates that the bullet is decelerating.
Step 4: Calculate the time taken (t):
To find the time taken to stop, we can use the equation:
v = u + at
Since v = 0 m/s and u = 33 m/s, we can solve for t:
0 = 33 + (-7785)t
Solving for t:
7785t = -33
t = -33 / 7785 ≈ -0.0042 seconds
Since time cannot be negative, the negative sign indicates the direction of deceleration. Therefore, the time taken to stop is approximately 0.0042 seconds.
In summary:
- The deceleration of the bullet is approximately -7785 m/s^2.
- The time taken to stop is approximately 0.0042 seconds.