Calculating Speed for a Bullet to Pass Through 10 Planks

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To determine the speed required for a bullet to pass through 10 planks, it is established that the bullet's final speed squared is proportional to the distance penetrated. Using the equation v² - u² = 2as, where the initial speed (u) is 10 m/s, the calculation shows that v² must equal 1000 for 10 planks. This leads to the conclusion that the necessary speed is 10 times the square root of 10. The discussion confirms the validity of this approach and suggests an alternative method using the work-energy theorem. The calculations and reasoning presented are sound for solving the problem.
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Homework Statement


A gunman shot a bullet with a speed of 10ms-1 which just penetrates into a plank of wood. So with what speed should he fire the bullet so that it passes through 10 similar planks?


Homework Equations


Newtons equations of motion.


The Attempt at a Solution


v2 - u2 = 2as
v2 is directly proportional to s

So,
v21/v22 = s1/s2

That means
v22 = 10*10*10
Therefore
v = 10 root 10



Well that's what I have done but I aint sure!
 
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Welcome to PF!

Hi The legend! Welcome to PF! :smile:

(have a square-root: √ :wink:)
The legend said:
v2 - u2 = 2as
v2 is directly proportional to s
…
v = 10 root 10

Yes, that's fine! :smile:

(btw, you could also have used the work-energy theorem … change in KE = work done = force x distance, is proportional to distance :wink:)
 

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