A bullet of mass,0.006kg traveling at 180m/s penetrates deeply into the target and it brought to rest in 0.01seconds ;calculate (I)the distance of penetration of the target.
We can use the equation:
force = mass x acceleration
since we know the mass of the bullet and the time it takes to come to rest in the target, we can calculate the force exerted on the bullet:
force = mass x acceleration
force = 0.006kg x (180m/s ÷ 0.01s)
force = 1080N
The force exerted on the bullet is the same force exerted by the bullet on the target. We can use this force and the formula for work (W = force x distance) to find the distance of penetration:
work = force x distance
distance = work ÷ force
distance = (0.5 x 0.006kg x (180m/s)^2) ÷ 1080N
distance = 0.097 m or 9.7 cm
Therefore, the distance of penetration of the target is 9.7 cm.
To calculate the distance of penetration, we can use the equation of motion:
vf^2 = vi^2 + 2ad
Where:
- vf is the final velocity (which is 0 m/s since the bullet is brought to rest)
- vi is the initial velocity of the bullet (180 m/s)
- a is the acceleration of the bullet (unknown in this case)
- d is the distance of penetration (unknown in this case)
Rearranging the equation, we have:
2ad = vf^2 - vi^2
Substituting the given values:
2 × a × d = 0 - (180)^2
2ad = - 32400
Since the bullet is brought to rest suddenly, we can assume the acceleration to be constant over the short time period. Let's assume the acceleration (a) remains constant.
Now, we can use another equation of motion to solve for the acceleration (a):
vf = vi + at
Here,
- vf is the final velocity (0 m/s)
- vi is the initial velocity (180 m/s)
- a is the acceleration (unknown)
- t is the time (0.01 s)
Rearranging the equation, we get:
a = (vf - vi) / t
Substituting the given values:
a = (0 - 180) / 0.01
a = -18000 m/s^2
Now we can substitute the value of a into the first equation:
2ad = -32400
2 × (-18000) × d = -32400
Simplifying:
-36000d = -32400
Dividing both sides by -36000 to isolate d:
d = -32400 / -36000
d = 0.9 m
Therefore, the distance of penetration of the target is 0.9 meters.