A bullet is fired from a rifle, emerging at 340 m/s. It strikes a sandbag some distance away, having lost 10% of its velocity due to air resistance. if it penetrates the sandbag to a depth of 12 meters, how long did it take for the bullet to come to rest in the bag?
To find the time it took for the bullet to come to rest in the sandbag, we can start by calculating the initial velocity of the bullet before air resistance slowed it down.
Given:
Initial velocity of the bullet (before air resistance) = 340 m/s
Velocity lost due to air resistance = 10% of the initial velocity = 0.1 * 340 = 34 m/s
Effective velocity of the bullet after air resistance = 340 - 34 = 306 m/s
Using the formula for constant acceleration:
Final velocity² = Initial velocity² + 2 * acceleration * distance
Let's assume the bullet came to rest inside the sandbag. In that case, the final velocity of the bullet would be 0 m/s.
0 = 306² + 2 * acceleration * 12
Rearranging the equation:
2 * acceleration * 12 = -306²
Now let's solve for acceleration:
acceleration = (-306²) / (2 * 12)
acceleration ≈ -7695 m/s²
The negative sign indicates that the bullet is decelerating.
Finally, we can find the time it took for the bullet to come to rest by using the equation:
Final velocity = Initial velocity + (acceleration * time)
0 = 306 + (-7695) * time
Rearranging the equation:
time = -306 / (-7695) = 0.0398 seconds
Therefore, it took approximately 0.0398 seconds for the bullet to come to rest in the sandbag.
To determine the time it took for the bullet to come to rest in the sandbag, we can use the equation of motion:
v^2 = u^2 + 2as
Where:
v = final velocity (0 m/s, since the bullet comes to rest)
u = initial velocity of the bullet (340 m/s)
a = acceleration (due to air resistance, which decelerates the bullet)
s = displacement (12 meters, as the bullet penetrates the sandbag)
Since the bullet loses 10% of its velocity due to air resistance, the final velocity becomes 90% of the initial velocity:
v = 0.9 * u
Plugging in the given values into the equation of motion, we can solve for acceleration:
0^2 = (0.9u)^2 + 2a(12)
Simplifying this equation:
0 = 0.81u^2 + 24a
Since we know the initial velocity (u = 340 m/s), we can substitute it into the equation:
0 = 0.81 * (340)^2 + 24a
By solving this equation, we can find the value of acceleration (a).
6/1000s
In the sandbag, the average velocity was 1/2 (340*.9)
time in the sandbag= distance/avgvelocity
solve for time.