Calculating Speed for a Bullet to Pass Through 10 Planks

[The legend]

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!

 

[tiny-tim]

Welcome to PF!

Hi The legend! Welcome to PF!

(have a square-root: √ )

v² - u² = 2as
v² is directly proportional to s
…
v = 10 root 10

Yes, that's fine!

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