Correct Answer - Maximum height is 122.5 m and total time si % s+5s =10s

Accrding to the equation of motion under gravity

`v^(2)-u^(2)=2gs`

where

u= intial velocity of the ball

v= final velocity of the ball

s= Height achieved by the ball

g= Acceleration due to gravity

At maximum height , final velocity of the ball is zero ,i.e., v=0

u=49 m/s

During upward , g=-`9.8ms^(-2)`

let h be the maximum height attained by the ball

Hence ,

`0-49^(2)=2xx9.8xxh`

`implies h=49^(2)//(2xx9.8)`

`implies h=2401//19.6 =1225.5`

Let t be the times taken by the ball to reach the height 122.5 m. then according to the equation of motion :

v=u+gt

We get

`0=49+txx)-9.8)`

`9.8 t=49`

`t=49//9.8=5s`

Also ,

time of ascent = Time of descent

therefore , total time taken by the ball to return `=5+5=10 s`