A body is thrown vertically upwards from A, the top of the tower, reaches the ground in time t₁ . If it is thrown vertically downwards from A with the same speed, it reaches the ground in time t ₂ . If it is allowed to fall freely from A , then the time it takes to reach the ground is given by

Step-by-step solution

Let the body is projected vertically upwards from A with a speed u₀ Using equation, s = ut + 1 2 at ² For case (1)- h = u ₀ t ₁- 1 2 gt ₁² (1) For case (2) - h = u ₀ t ₂- 1 2 gt ₁² Subtracting eq (2) from (1), we get array l 0= u ₀ ( t ₂+ t ₁ )+ 1 2 ~g ( t ₂²- t ₁² ) u ₀= 1 2 ~g ( t ₁- t ₂ ) array Putting the value of u ₀ in eq (2), we get - h =- ( 1 2 ) g ( t ₁- t ₂ ) t ₂- ( 1 2 ) gt ₂² h = 1 2 ~g ( t ₁ t ₂ ) For case 3, u ₀=0, t =? - h =0 t - ( 1 2 ) gt ² h = ( 1 2 ) gt ² Comparing eq. (4) and (5), we get 1 2 gt