Question

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 $m/s^2$):

• A. 17.6 m
• B. 12.8 m
• C. 8 m
• D. 4.8 m

Answer 1

The correct option is D 4.8 m

From work energy theorem

For upward motion

$\frac{1}{2}m(16{)}^2=mgh+W...........(i)$(workdone against resistance)

For downward motion

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

From (i) and (ii)

$\frac{1}{2}m[{16}^2-8^2]=2mgh$

$\frac{1}{2}[256-64]=2\times 10\times h$

$h=4.8m$