Question

If air drag is not neglected, then which is greater time of ascent or time of descent?

Answer 1

When body is moving upward, time of ascent is given by:-

As we know that gravity is acting down-ward & so does the force due to air resistance, hence for total acceleration we can imply

$a_{total}=g+\frac{R}{m}$ {R: Resistive force due to air}

$\therefore \Rightarrow t_a=\frac{v}{(g+\frac{R}{m})}$----------1 {v:Initial velocity}

Now, for time period of body in descent the air resistive force is acting in upward direction because the gravity is acting in downward direction.

$\therefore$ for total acceleration in this case we get

$a_{total}=g-\frac{R}{m}$

$\Rightarrow t_d=\frac{v}{(g-\frac{R}{m})}$-----------2

From Statement 1 & 2, we get time of descent is greater.