a bullet leaves a rifle with a velocity of 200m/sec and strikes targt up to 4cm what velocity scould it have pierce the same block of wood up to 16cm?
i think it is just a hard Q.
To determine the velocity required for the bullet to penetrate the same block of wood up to 16cm, we can use the concept of kinetic energy.
Kinetic energy (KE) is defined as KE = 1/2 * m * v^2, where m is the mass of the bullet and v is its velocity.
First, let's assume that the mass of the bullet remains constant throughout this scenario. Therefore, we can simplify the equation by omitting the mass term.
For the first case, where the bullet penetrates the wood up to 4cm, the initial kinetic energy (KE1) can be calculated as KE1 = 1/2 * v1^2.
Now, for the second case, we need to find the required velocity (v2) that will allow the bullet to penetrate the wood up to 16cm. The kinetic energy required to achieve this penetration (KE2) can be calculated as KE2 = 1/2 * v2^2.
Since the same block of wood is being penetrated in both cases, we can set KE1 equal to KE2:
1/2 * v1^2 = 1/2 * v2^2.
To find the relationship between v1 and v2, we can calculate the ratio of the distances penetrated, expressed as:
(v2/v1)^2 = (16/4)^2.
Simplifying the equation gives:
(v2/v1)^2 = 4^2.
Taking the square root of both sides:
v2/v1 = 4.
Therefore, to penetrate the block of wood up to 16cm, the bullet should have a velocity four times greater than its initial velocity. Given that the initial velocity is 200m/sec, the required velocity to achieve a penetration of 16cm would be:
v2 = 4 * v1 = 4 * 200m/sec = 800m/sec.