A particle is projected vertically upwards with a speed of 16 m/s. After some time, when it again passes through the point of projection, its speed is found to be 8 m/s. It is known that the work done by air resistance is same during upward and downward motion. Then the maximum height attained by the particle is : (take g = 10 m/s²\)

8 m

Work-Energy Theorem

(1) for upward motion :

\(\frac{1}{2}*m*16^2 = mgh + W\) ... (A)

(2) for downward motion :

\(\frac{1}{2}*m*8^2 = mgh - W\) ... (B)

From (A) and (B) : 

\(\frac{1}{2}[16^2 + 8^2] = 2 gh\)

\(\Rightarrow h = 8 \text{ m}\)