A bullet loses 1 n th of its velocity passing through one plank. Considering uniform retardation, the number…

A bullet loses 1nth of its velocity passing through one plank. Considering uniform retardation, the number of such planks that are required to stop the bullet can be:
  1. Infinite
  2. n
  3. n22n-1
  4. 2n2n-1

Solution

 
Let t be the thickness of the plank

υ01-1n2=υ02-2at

 2at=υ02-υ021-1n2

If m number of planks are required to stop a bullet, then

0=υ02-2atm

 m=υ022at

=υ02υ021-1-1n2

=n2n2-n-12=n22n-1

Asked in: JEE Main 2014 (19 Apr Online)

Practice more Motion In One Dimension questions on Aicharya