Arun
Last Activity: 6 Years ago
Let a = acceleration/deceleration of the bullet inside the plank.
let s = thickness of the plank
let the initial velocity of the bullet before hitting the plank: = u
final velocity = v = u - u/n = u (n-1)/n
v² = u² + 2 a s
u² (n-1)² / n² = u² + 2 a s
2 a s = u² [ (n-1)² - n² ] / n² = - (2n - 1) u² / n²
a = - (2 n - 1) u² / (n² 2 s)
let S be the thickness of the N planks kept one after another to stop the bullet. The deceleration is the same. The initial velocity is the same.
v² = 0 = u² - 2 S * (2 n - 1) u² / (n² 2 s)
1 = S/s * (2 n -1) / n²
N= S/s = n² / (2 n - 1) = 1/2 * [ (2n² -n) + n ] / (2n -1)
= 1/2 * [ n + n / (2n -1) ]
= n/2 + n/(4n-2)
the second term above is between 0 and 1.
N = number of planks = [ n/2 ] + 1
where [ n/2 ] is the greatest integer function for n/2.
now in this question
n = 2
hence
total number of plank required = [2/2] + 1
= 1 + 1
= 2
