MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade: 12th pass
        A bullet loses 1/n of its velocity in passing through a plank . what is the least no of planks required to stop the bullet?
2 years ago

Answers : (1)

Arun
23036 Points
							Dear Aditi

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.
=====================================
let
n = 1,  S/s = 1 :  so one plank.
n = 2,  S/s = 4/3:  so two planks needed.
n = 3,    S/s = 9/5 , so two planks needed.
n = 4,  S/s = 16/7 ,  so  three planks are needed.
n = 10,  S/s = 100/19 :  six needed.
n =  11,  S/s = 121/21 :  six needed.
n = 21.    S/s = 21² / (41) = 10.75.  so eleven  planks needed.
 
Regards
Arun (askIITians forum expert)
2 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


Course Features

  • 101 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 110 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details