Block slipping against two blocks

[Vibhor]

Homework Statement

In the setup , block C remains at rest and block A move towards left when system is released . If velocity of A is 'u' towards left at an instant , what is the vertical component of velocity with which B descends .What is the horizontal component of velocity of B at this instant ?

Ans : Vertical component of velocity = (u/2)tanθ₁

Horizontal component of velocity = (u/2)

Homework Equations

The Attempt at a Solution

[/B]
Block B is constrained to move along the contact surface with C . From the geometry it can be seen that when B moves vertically down by distance 'x' ,it is constrained to move by a distance xcotθ₁ towards left .

By similar argument , suppose C is not present ,and B is somehow constrained to move exclusively in only vertical direction .If B moves down by a distance 'x' , A moves towards left by a distance xcotθ₂ .

Combining the two effects we can say if B moves down by a distance 'x' , A moves towards left by a distance xcotθ₁ +xcotθ₂ .

Similarly If vertical speed of B is 'v' then speed of A is u = vcotθ₁ +vcotθ₂ .

Now in the question we are given 'u' and asked to find 'v' and 'vcotθ₁' .

I am not sure how do I get 'v' and 'vcotθ₁' in terms of u .

Is the book answer correct ?

Any help is appreciated .

Thanks .

 

[haruspex]

I agree with your answer. It clearly has to involve θ₂. It looks like the problem was originally for two equal angles and the answer was not updated correctly when they were made different angles.