In projectile motion two particles of masses m ₁ and m₂ have velocities V ₁ , and V ₂ respectively at time t =0 . Their velocities become V ₁ ^ and V ₂ ^ at time 2 t while still moving in air. The value of [ (m₁ V₁ ^ +m₂ V₂ ^ )- (m₁ V₁ +m₂ V₂ ) ] is ( g = acceleration due to gravity)

Step-by-step solution

aligned & F _ ext = ( m ₁+ m ₂ ) g & P t = [ ( m ₁ ~V ₁^ + m ₂ ~V ₂^ )- ( m ₁ ~V ₁ + m ₂ ~V ₂ ) ] 2 t -0 aligned F _ ext = P t (m₁+m₂ ) g= [ (m₁ ~V ₁^ + m ₂ ~V ₂^ )- ( m ₁ v ₁ + m ₂ ~V ₂ ) ] 2 t [ ( m ₁ ~V ₁^ + m ₂ ~V ₂^ )- ( m ₁ ~V ₁ + m ₂ ~V ₂ ) ]=2 (m₁+m₂ ) g t