# Newton Laws of motion question

1. ### Pranav-Arora

1. The problem statement, all variables and given/known data
A rod AB is shown in figure. End A of the rod is fixed on the ground. Block is moving with velocity √3 m/s towards right. The velocity of end B when rod makes an angle of 60o with the ground.

2. Relevant equations

3. The attempt at a solution
I assumed that at any instant the distance of A from block is x and distance of B from ground is y. The length of rod is l.
l^2=x^2+y^2
Differentiating with respect to time.
0=2x(dx/dt)+2y(dy/dt)
y=xtan(60o)
dx/dt=√3 m/s
Solving, i get

(dy/dt)=-3 m/s
But that's not correct, the answer says its 2 m/s. I don't seem to get where i am wrong.
Any help is appreciated.

Thanks!

2. ### Infinitum

854
Hi Pranav!

Are you sure about that step?

$$0 = 2x\sqrt{3} + 2\sqrt{3} x \frac{dy}{dt}$$

Last edited by a moderator: Jun 19, 2012
3. ### Pranav-Arora

Oh yes, sorry, my mistake, i wrote tan60=1/√3. :tongue:

But now i get (dy/dt)=-1.

4. ### Infinitum

854
Yes. That's correct. So, whats the velocity of the end B of the rod now?

5. ### Pranav-Arora

Isn't (dy/dt) the velocity of the end B?

6. ### Infinitum

854
That is the vertical component of B's velocity

7. ### Pranav-Arora

Ah i get it, thanks for the help Infinitum!
I shouldn't be studying Physics at midnight.

8. ### Infinitum

854

Good night, then

9. ### Pranav-Arora

Hehe, no, i am posting one more question and then i will go to sleep. :D