A stone thrown down with a seed u takes a time t₁ to reach the ground, while another stone, thrown upwards from the same point with the same speed, takes time t₂ . The maximum height the second stone reaches from the ground is

Step-by-step solution

- h =- Ut ₁+ -1 2 ~g t ₁ ² ~h = Ut ₁+ 1 2 ~g t ₁ ² . (1) - h = Ut ₂- 1 2 ~g t ₂ ² (2) Ut ₁+ Ut ₂= 1 2 ~g t ₂ ²- 1 2 ~g t ₁ ² ( from 1 & 2) U ( t ₁+ t ₂ )= g 2 ( t ₂- t ₁ ) ( t ₁+ t ₂ ) U = g 2 ( t ₂- t ₁ ) aligned & Max height = h + U ² 2 ~g &=( h )+ U ² 2 ~g &= U t ₁+ 1 2 ~g t ₁²+ U ² 2 ~g &= g 2 t ₁ ( t ₂- t ₁ )+ 1 2 ~g t ₁²+ 1 2 ~g g ² 4 ( t ₂- t ₁ )² &= g 2 ( t ₂- t ₁ ) t ₁+ gt ₁ ² 2 + g 8 ( t ₂- t ₁ )² &= ( g 2 ) ( t ₂ t ₁- t ₁ ² )+ t ₁ ²+ ( t ₂- t ₁ )² 4 &= ( g 2 ) 4 t ₂ t ₁-4 t ₁ ²+4 t ₁ ²+ t ₂²+ t ₁²-2 t ₁