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  4. A particle is projected vertically upwards with a speed of 16 m s- 1 , after some time, when it again passes through the point of projection, its speed is found to be 8 m s- 1 . It is found that the work done by air resistance is the same during upward and downward motion. Then the maximum height attained by the particle is -

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Q. A particle is projected vertically upwards with a speed of $16 \, m \, s^{- 1}$ , after some time, when it again passes through the point of projection, its speed is found to be $8 \, m \, s^{- 1}$ . It is found that the work done by air resistance is the same during upward and downward motion. Then the maximum height attained by the particle is -

NTA AbhyasNTA Abhyas 2022Work, Energy and Power

Solution:

From work energy theorem
for upward motion,
$\frac{1}{2}m \, \left(16\right)^{2}=mgh+W$
for downward motion
$\frac{1}{2}m \, \left(8\right)^{2}=mgh \, - \, W$
$h=8 \, m$