Two balls are thrown from an inclined plane at angle of projection with the plane, one up the incline and other down the incline as shown in figure ( T stands for total time of flight, h₁ and h₂ are maximum hight from incline, R₁ and R₂ are ranges, v_ t₁ and v_ t₂ are the velocities of the particles at their maximum heights) :

Step-by-step solution

h_ 1 max = (v₀ )^2 2 g =h_ 2 max (a) is correct T₁= 2 v₀ g =T₂= (b) is correct R₁= (v₀ ) T₁- 1 2 g T₁^2R₂= (v₀ ) T₂+ 1 2 g T₂^2 (R₂-R₁ )=g T₁^2 (c) is correct v_ t₁ and v_ t₂ are the velocities of the particles at Their maximum heights. Let the particles reach Their maximum heights at time t₁ and t₂ respectively Hence aligned & 0= (v₀ )-(g ) t₁ & =t₁= v₀ g aligned Similarly t₂= v₀ g . Hence t₂=t₁ Hence v_ t₁ =v₀ -(g ) t₁v_ t₂ =v₀ +(g ) t₂