First slide

Rectilinear Motion

Question

A particle is thrown upwards from ground. It experiences a constant air resistance force which can produce a retardation of 2 m/s². The ratio of time of ascent to the
time of descent is

Difficult

A

$1 : 1$
B

$\sqrt{\frac{2}{3}}$
C

$\frac{2}{3}$
D

$\sqrt{\frac{3}{2}}$

Solution

Let a be the retardation produced by resistive force, ta and td be the time ascent and descent respectively.
If the particle rises up to a height h
$\begin{array}{l} Then h = \frac{1}{2} (g + a) t_{a}^{2} and h = \frac{1}{2} (g - a) t_{d}^{2} \\ ∴ \frac{t_{a}}{t_{d}} = \sqrt{\frac{g - a}{g + a}} = \sqrt{\frac{10 - 2}{10 + 2}} = \sqrt{\frac{2}{3}} \end{array}$

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