Answer to Question #320067 in Quantum Mechanics for Ndina

Question

Consider an object projected straight upward from z=0 with an initial speed of u. Assume that the object is subjected to a linear drag force of the form D=-mKv

a)From the first principle show that t=1/K In(g+Ku/g+Kv) and use this result to find the time taken to reach the maximum height

b)Find the expression for the speed v as a function of time and find the limiting speed

Answer 1

Answer

a) for these type of D=-mKv and t=1/K In(g+Ku/g+Kv) case force is calculate by using by second law of newton

$F=ma\\ m\frac{dv}{dt}=ma$

b) putting at value of t=1/K In(g+Ku/g+Kv) we get expression for velocity of particle.