Question

A body of mass $m$ is thrown vertically up with a velocity $u$. If the resistance force due to air is $f$, the time of ascent of the body is

• A. $\frac{u}{g+f}$
• B. $\frac{mu}{mg+f}$
• C. $\frac{u}{g-f}$
• D. $\frac{mu}{mg-f}$

Answer 1

The correct option is B $\frac{mu}{mg+f}$

Forces acting on the body are gravitational and frictional forces which provide retardation.
$ma=mg+f$
$a=\frac{mg+f}{m}$
We have
$v=u+at$
$0=u-\frac{mg+f}{m}\left(t\right)$
$t=\frac{mu}{mg+f}$
Option B.