A ball is thrown vertically upward with speed `10 m//s` and it returns to the ground with speed `8 m//s`. A constant air resistance acts. The minimum height attained by the ball is

Explanation

Let the height attained by the ball be `h`.
Upward motion: `K_1+U_1=K_2+U_2+W_R`
`(1)/(2)m(10)^2=mgh+Rh` .(i)
Downward motion : `K_1+U_1=K_2+U_2+W_R`
`mgh=(1)/(2)m(8)^2+Rh` .(ii)
Substracting (ii) from (i) we get
`(1)/(2)m(10)^2-mgh=mgh-(1)/(2)m(8)^2`
`4gh=(10)^2+(8)^2=164`
`h=(164)/(40)=4.1m`