A bullet of 0.06kg travelling at 120m/s penetrates into a fixed target and is brought to rest in 0.01s. The distance through which it penetrates is:
Answer is 60cm
average velocity = (initial + final) / 2 = (120 + 0) / 2 = 60 m/s
distance = velocity * time = 60 m/s * 0.01 s
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To find the distance through which the bullet penetrates, we can use the equation for average acceleration:
acceleration = (final velocity - initial velocity) / time
Given:
mass (m) = 0.06 kg
initial velocity (u) = 120 m/s
final velocity (v) = 0 m/s
time (t) = 0.01 s
Since the bullet is brought to rest, the final velocity is 0 m/s.
Using the equation for acceleration, we can solve for the acceleration:
acceleration = (0 - 120) / 0.01
acceleration = -12000 m/s^2
The force acting on the bullet can be calculated using Newton's second law:
force = mass × acceleration
force = 0.06 kg × -12000 m/s^2
force = -720 N
Now, using the formula for work done by a force:
work = force × distance
Since the bullet stops completely, all its initial kinetic energy is converted into work done to overcome the resistance of the fixed target. So, the work done is equal to the initial kinetic energy:
work = (1/2) × mass × initial velocity^2
work = (1/2) × 0.06 kg × (120 m/s)^2
work = 432 J
Since work is equal to force times distance, we can solve for the distance:
distance = work / force
distance = 432 J / -720 N
distance = -0.6 m
The distance through which the bullet penetrates is -0.6 m. However, distance cannot be negative. Therefore, the magnitude of the distance is 0.6 m or 60 cm.
To find the distance through which the bullet penetrates the fixed target, we can use the formula for average acceleration:
average acceleration (a) = (change in velocity)/(time)
Given:
Mass of the bullet (m) = 0.06 kg
Initial velocity (u) = 120 m/s
Final velocity (v) = 0 m/s (brought to rest)
Time taken (t) = 0.01 s
First, we need to find the change in velocity using the equation:
change in velocity = (final velocity) - (initial velocity)
= v - u
= 0 - 120
= -120 m/s
Next, we substitute the values into the average acceleration formula:
a = (change in velocity)/(time)
a = -120/0.01
= -12000 m/s^2
Now, we can use the formula for distance traveled (d) during constant acceleration:
d = (initial velocity * time) + (0.5 * acceleration * time^2)
Substituting the given values:
d = (120 * 0.01) + (0.5 * -12000 * 0.01^2)
= 1.2 - 0.6
= 0.6 meters
Finally, converting the distance to centimeters:
1 meter = 100 centimeters
Therefore, the distance through which the bullet penetrates the fixed target is:
0.6 meters * 100 = 60 centimeters