Question

A bullet passes through two planks in succession, its original velocity is 120 m/sec and it loses a velocity of 20 m/sec in penetrating each plank. find ratio of thickness of two planks, assuming that they offered the same resistance.​

Answer 1

Let us assume that the thickness of the plank be s and acceleration provided by each plank is a

Now, using equation of motion

 v  

2

−u  

2

=2as

u  

2

=−2as

Now, let the number of planks required be n,

So, u  

2

=−2ans

n=  

2as

−u  

2

 

​  

......(I)

Now, the bullet loses its speed by  

20

1

​  

 on passing through plank

So, the final speed of the bullet when it leaves one plank is

 v=u−  

20

u

​  

 

v=  

20

19u

​  

 

 

Now, again using equation of motion

v  

2

−u  

2

=2as

Now, put the value of v

 (  

20

19

​  

u)  

2

−u  

2

=2as

 

400

361

​  

u  

2

−u  

2

=2as

−  

400

39u  

2

=2as

Now, put the value of 2as in equation (I)−  

400

39u  

2

−u  

2

 

n=10.26

 n≃11

So, the number of planks required is 11