A bullet is moving with velocity u after emerging from a plank
its velocity reduces by u/20 then find the total number of planks required to stop this bullet?
u - u/20 = 19u/20 = .95u
.95² = .9025
the bullet loses about 10% of its energy (kinetic), as work passing through the plank
it should stop in the 11th plank
To determine the total number of planks required to stop the bullet, we need to calculate the velocity reduction per plank and then divide the initial velocity of the bullet by this reduction.
The velocity reduction per plank is given as u/20, where u is the initial velocity of the bullet.
To find the total number of planks needed, we divide the initial velocity u by the velocity reduction per plank (u/20):
Total number of planks = u / (u/20) = u * (20/u) = 20
Therefore, the total number of planks required to stop the bullet is 20.
To find the total number of planks required to stop the bullet, we need to find how many times the velocity is reduced by u/20 until it reaches zero.
Let's break down the problem step by step:
Step 1: Determine the first reduction in velocity.
After the bullet emerges from the plank, its velocity reduces by u/20. So, the new velocity becomes (u - u/20) = (19u/20).
Step 2: Calculate the subsequent reductions in velocity.
In each subsequent reduction, the velocity decreases by u/20. So, the new velocity after the second reduction becomes (19u/20 - u/20) = (18u/20).
Step 3: Repeat Step 2 until the velocity reaches zero.
Continue reducing the velocity by u/20 until it becomes zero. Each time, subtract u/20 from the previous velocity. We repeat this process until the velocity reaches zero.
Step 4: Determine the number of planks.
The number of planks required is the number of reductions performed.
To summarize:
- Initial velocity of the bullet: u
- Velocity after the first reduction: (19u/20)
- Velocity after the second reduction: (18u/20)
- Velocity after the third reduction: (17u/20)
- ...
- Velocity after the nth reduction: (u - (n * u/20))
The total number of planks, n, can be calculated by finding the value of n for which the velocity becomes zero:
(u - (n * u/20)) = 0
Simplifying the equation:
u - (n * u/20) = 0
u(1 - n/20) = 0
Since u cannot be zero (otherwise the bullet would not be moving), we solve for (1 - n/20) = 0:
1 - n/20 = 0
n/20 = 1
n = 20
Therefore, it will take a total of 20 planks to stop the bullet.