Rankers Physics
Topic: Kinematics
Subtopic: Motion Under Gravity

A particle is thrown upwards from ground. It experience 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 : [g = 10 m/s²]
1 : 1
\[\sqrt{\frac{2}{3}}\]
2/3
\[\sqrt{\frac{3}{2}}\]

Solution:

Effective accelerations:
- Ascent: \( a_{\text{eff}} = g + a = 10 + 2 = 12 \, \text{m/s}^2 \)
- Descent: \( a'_{\text{eff}} = g - a = 10 - 2 = 8 \, \text{m/s}^2 \)

Ratio of times:
\[
\frac{t_a}{t_d} = \sqrt{\frac{a'_{\text{eff}}}{a_{\text{eff}}}} = \sqrt{\frac{8}{12}} = \sqrt{\frac{2}{3}}
\]

The ratio of time of ascent to time of descent is √(2/3).

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