a bullet fired into a fixed target loses half of its velocity in penetrating 15cm.how much further will it penetrate before coming to rest?
options:
1.5cm
2.15cm
15
3/4 of the initial kinetic energy is used up going the first 15 cm. There is enoough left to penetrate 1/3 as far (5 cm). This assumes that the force resisting penetration is constant.
i think it should be 1/3rd if 15 i.e. cm but not sure...
i also don't know correctly but if anyone knows please let me know....
5cm
5 cm..Use v^2-u^2=2as...Hope u will get the answer...or do it by using the method of
conservation of energy
To solve this problem, we can use the concept of work-energy theorem. According to the theorem, the work done on an object is equal to the change in its kinetic energy.
First, let's assume the initial velocity of the bullet is V and it loses half of its velocity to reach V/2. The initial kinetic energy is given by (1/2)mV^2, where m is the mass of the bullet.
Since the bullet loses half of its velocity in penetrating 15cm, we can write:
(1/2)m(V/2)^2 = W
Where W is the work done by the resisting force to bring the bullet to rest.
Now, let's find the value of work done. The work done is given by:
W = Force * Distance
Since the bullet is penetrating a fixed target, the force on it is constant. Therefore, we can rewrite the equation as:
W = F * d
Where F is the force and d is the distance the bullet has penetrated before coming to rest.
To find the distance, we can rearrange the equation:
d = W / F
Now, let's consider the initial velocity of the bullet. Assuming its initial kinetic energy is fully converted to work done, we can write:
(1/2)mV^2 = W
Rearranging the equation, we get:
W = (1/2)mV^2
Substituting this value into the previous equation, we have:
d = [(1/2)mV^2] / F
Since we know the bullet loses half its velocity, we can conclude that the final velocity is zero. Therefore, the work done is equal to the initial kinetic energy. Thus, we can rewrite the equation as:
d = (1/2)mV^2 / F
The problem provides the information that the bullet loses half of its velocity in penetrating 15cm. However, we do not have values for the mass of the bullet or the force acting on it. Without these values, we cannot calculate the distance the bullet will penetrate further before coming to rest.
Therefore, we cannot determine whether the bullet will penetrate 1.5cm or 15cm further before coming to rest.