Projection From Top Of A Tower

Projection From Top  Of A Tower

(EXPRESSION FOR HEIGHT OF TOWER):
Consider a tower of height H. Suppose a body is projected upwards vertically with initial velocity from the top of tower. Suppose it reaches to a displacement x above the tower and there after reaches the foot of the tower. Let t be the total time of travel.
Now, considering the total path of the body,the motion parameters are as follows.
    Initial velocity of the body = u
    Net displacement of body = S =+x-x-H =-H 
    Time of travel = t
    we know that, \( S = ut + \frac{1} {2}at^2 \)
         
   
    Here,                                    
    a=-g, SH, u = u, t = t
     \( \therefore - H = ut - \frac{1} {2}gt^2 \) 
     \( \therefore H = \frac{1} {2}gt^2 - ut \)