A body is thrown vertically upwards from A, the top of a tower. It reaches the ground in time t1. lf it is thrown vertically downwards from A with the same speed, it reaches the ground in time t2. If it is allowed to fall freely from A, then the time it takes to reach the ground is given by

Suppose the body be projected vertically upwards from A with a speed u0. Using equation s=ut+12at2, we get  For first case: −h=u0t1−12gt12    ......(i) For second case: −h=−u0t2−12gt22   ......(ii)From (i) and (ii) we geth=12gttt2    ……(iii) For third case: u=0,t=?−h=0×t−12gt2  or  h=12gt2  …..(iv)Combining Eq. (iii) and Eq. (iv), we get12gt2=12gt1t2  or  t=t1t2