Sliding Rod Problem: Find Velocity of Particle A at H=30°"

[subhradeep mahata]

Homework Statement

Two particles A and B are connected by a rigid rod AB which slides along two mutually perpendicular rails as shown.

H is the angle between point B and the horizontal rod. At an instant, when H=30°, the velocity of B is 10m/s towards left, and velocity of A is upwards. Find the velocity of A at that instant.

Homework Equations

The Attempt at a Solution

Now, I don't know if it is a rubbish method or not, I tried to solve it by forming a vector triangle as shown.

(where Vb and Va are velocities of B and A at that instant)
Now, V_a=V_b * tan 30° = 10/√3 m/s
But the correct answer according to my book is 10√3 m/s.
I don't want you to post the exact solution, but I request you to point out what went wrong in my method. Thanks.

 

[haruspex]

point out what went wrong in my method.

You do not provide a reason as to why it should be right. Without some basis, it is just a guess.

The trick with these kinematic problems is to think about the lengths that stay constant. In this case it is the length of the rod.
What does that tell you about the components of the two velocities in the direction of the rod?

 

[subhradeep mahata]

Okay, so the component of the velocities of b and a in the direction of the rod are 10 cos30° and -xcos60° respectively where x is velocity of a. But I don't understand how they are related to the length of rod being constant.

 

[haruspex]

Okay, so the component of the velocities of b and a in the direction of the rod are 10 cos30° and -xcos60° respectively where x is velocity of a. But I don't understand how they are related to the length of rod being constant.

Suppose B were moving at that speed in that direction (towards A), but A does not move. What would happen to the rod?

 

[Ganit]

Pythagoras + calculus = solution of ur problem

 

[haruspex]

Pythagoras + calculus = solution of ur problem

No, it's easier than that.

 

[Ganit]

Okay, so the component of the velocities of b and a in the direction of the rod are 10 cos30° and -xcos60° respectively where x is velocity of a. But I don't understand how they are related to the length of rod being constant.

Try thinking that there is no rod but the there is constraint on particles 'A' an 'B' to move in such a way to keep distance between them constant then what would that Constraint be

 

[SammyS]

Try thinking that there is no rod but the there is constraint on particles 'A' an 'B' to move in such a way to keep distance between them constant then what would that Constraint be

Hello @Ganit .


@haruspex is giving help appropriate for the OP who apparently is a High School student.

It may be that speaking in terms of "constraints", etc. is over OP's head.