Question

A body is thrown vertically upwards. If air resistance is to be taken into account, then the time during which the body rises is

• A. Equal to the time of fall
• B. Less than the time of fall
• C. Greater than the time of fall
• D. Twice the time of fall

Answer 1

Answer: (B)

Less than the time of fall

Answer 2

Let the initial velocity of ball be u

Time of rise $t_{1} = \frac{u}{g + a}$and height reached

Time of fall $t_{2}$ is given by

$\frac{1}{2}(g - a)t_{2}^{2} = \frac{u^{2}}{2(g + a)}$

$\Rightarrow t_{2} = \frac{u}{\sqrt{(g + a)(g - a)}} = \frac{u}{(g + a)}\sqrt{\frac{g + a}{g - a}}$

$\therefore$ $t_{2} > t_{1}$ because $\frac{1}{g + a} < \frac{1}{g - a}$