A ball is projected vertically upwards from ground. It reaches a height ' h ' in time t₁ , continues its motion and then takes a time t₂ to reach ground. The height h in terms of g, t₁ and t₂ is (g= acceleration due to gravity)

Step-by-step solution

We know, S = ut + 1 2 at ^2 The total time required for the ball to go up and reach the ground is t=t₁+t₂ , and the total displacement is zero. aligned & 0= u ( t ₁+ t ₂ )+ 1 2 ~g ( t ₁+ t ₂ )^2 & u = 1 2 ~g ( t ₁+ t ₂ ) aligned The displacement in time t₁ is aligned h & = 1 2 ~g ( t ₁+ t ₂ ) t ₁- 1 2 gt ₁^2 ~h & = 1 2 gt ₁ ( t ₁+ t ₂- t ₁ ) h & = 1 2 gt ₁ t ₂ aligned