Engineering
Physics
Straight Line Motion
Projectile Motion
Circular Motion in Vertical Plane
Question

Three particles are projected in 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. Then the relation among the projection speeds of the three particles is

u32=2u1u2

u32=u12+u22

u3 = u1 + u2

1u3=1u1+1u2

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Solution
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R =u22g(1+sinα)

⇒u22= Rg(1 + sinα)......(i)

R =u12g(1−sinα)

⇒u12= gR (1 – sinα)......(ii)

2Rcos α=u32g

⇒u32= 2Rg cos α........(iii)

Now, u1u2 =Rg1−sin2α

= Rg cosα=u322

∴u32=2u1u2