On piercing a distance of 15cm in a wooden block a bullet losses of its initial velocity before coming to rest the further distance travelled by it is
Ans:5cm
To find the further distance traveled by the bullet after losing all of its initial velocity, we need to understand the concept of projectile motion and energy conservation.
When the bullet is first fired into the wooden block, it has an initial velocity. As it travels through the wood, it experiences resistance due to friction and air drag, causing its velocity to gradually decrease. Eventually, the bullet comes to a complete stop when all of its initial velocity is lost.
In this scenario, we are given that the bullet pierces a distance of 15 cm into the wooden block before coming to rest. Let's assume that the bullet's initial velocity is v.
To find the further distance traveled by the bullet after losing all of its initial velocity, we can consider the conservation of energy. At the point where the bullet comes to rest, all of its kinetic energy has been converted into work done against the friction and resistance forces.
The work done on the bullet can be calculated using the formula:
Work = Force * Distance
Assuming that all the deceleration forces acting on the bullet are constant, 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
a = acceleration (deceleration in this case)
s = distance (piercing distance into the wooden block)
From the equation of motion, we can determine the acceleration:
0 = u^2 - 2as
2as = u^2
a = (u^2) / (2s)
Now, using the work-energy theorem, the work done on the bullet is equal to the change in kinetic energy:
Work = ΔKE
Work = Final KE - Initial KE
Since the bullet comes to rest, its final kinetic energy is zero:
Work = 0 - (1/2)mu^2
Now, substituting the value of acceleration into the work equation, we get:
Force * Distance = (1/2)mu^2
Distance = (1/2)mu^2 / Force
Since the distance traveled after coming to rest is the distance penetrated into the wooden block, the further distance traveled by the bullet is:
Further Distance = Distance - Distance penetrated
Further Distance = Distance - 15 cm
Further Distance = (1/2)mu^2 / Force - 15 cm
To calculate the exact further distance traveled, we need to know the values of initial velocity (u) and the deceleration forces acting on the bullet. Without this information, it is not possible to provide an exact numerical answer.
Therefore, based on the given information, we cannot determine the exact further distance traveled by the bullet.