Question

A particle m is thrown vertically upward with an initial velocity v. Assuming a resisting medium proportional to the velocity, where the proportionality factor is c, calculate the velocity with which the particle will strike the ground upon its return if there is a uniform gravitational field.

Answer 1

Answer:$v_0=v\sqrt{\frac{g-vc}{g+vc}}$

Explanation:

Given

v=initial velocity

resisting acceleration =cv

also gravity is opposing the upward motion

Therefore distance traveled during upward motion

$v^2_f-v^2=2as$

Where a=cv+g

$0-v^2=2(cv+g)s$

$s=\frac{v^2}{2(cv+g)}$

Now let v_0 be the velocity at the ground

$v^2_0-0=2(g-vc)s$

substituting s value

$v^2_0=v^2\frac{g-vc}{(cv+g)}$

$v_0=v\sqrt{\frac{g-vc}{g+vc}}$