Question

Three particles are projected in the air with the minimum possible speeds, such that the first goes from A to B, the second goes from B to C and the third goes from C to A. Points A and C are at the same horizontal level. The two inclines make the same angle a with the horizontal, as shown. The relation among the projection speeds of the three particles is​

Answer 1

Answer:

given = 3 particles

            possible speeds =  A to B , B to C , C to A

   

to find =  The relation among the projection speeds of the three particles is​?

solution  =

         ⇔   range (R) =  u²/ g(1 + sin∝)

         ⇔   u1² = Rg (1 - sin∝)...1

         ⇔   range (R) =  u²/ g(1 + sin∝)

         ⇔   u2² =  Rg (1 + sin∝).... 2

         ⇔   2Rcos∝ = u³/g

         ⇔   u3² = 2Rgcos∝.......3

         ⇔   u1u2 = Rg$\sqrt{1-sin²∝}$

         ⇔   Rg cos∝ = u²3/ 2

         ⇔   u²3 = 2u₁u₂

so the relation between the speeds is  u²3 = 2u₁u₂