A ball is released from rest from top of a tower. The retardation due to air resistance is bv, where b is 10 per second and velocity v is ms-1. The velocity of ball at t=110s is n27ms−1 The value of n (Given, e=2.7) is _________.

The acceleration of ball at instant t is a=g−bv∵ a=g−bv Or dvdt=g−bv or ∫0v dvg−bv=∫0t dt Or  −12[ln⁡(g−bv)]0v=[t]0t Or [ln⁡(g−bv)−ln⁡g]=−bt Or ln⁡g−bvg=−bt Or  1−bvg=e−bt or bvg=1−e−bt Or  v=gb1−e−bt=10101−1e =e−1e=2.7−12.7=727=n27∴ n=7