What is the velocity of the block when the angle between the string and horizontal is \(30^\circ\) as shown in the diagram?

          
1. \(v_B=v_P\)
2. \(v_B=\frac{v_P}{\sqrt{3}}\)
3. \(v_B=2v_P\)
4. \(v_B=\frac{2v_P}{\sqrt{3}}\)

The figure shows a rod of length 5 m. Its ends, A and B, are restrained to moving in horizontal and vertical guides. When the end A is 3 m above O, it moves at 4 m/s. The velocity of end B at that instant is:
         

1. 2 m/s

2. 3 m/s

3. 4 m/s

4. 0.20 m/s

If the block is being pulled by the rope moving at speed v as shown, then the horizontal velocity of the block is:

1.  v

2.  vcos$\mathrm{\theta }$

3.  $\frac{\mathrm{v}}{\cos \mathrm{\theta }}$

4.  $\frac{\mathrm{v}}{\sin \mathrm{\theta }}$

A rigid rod is placed against the wall as shown in the figure. When the velocity at its lower end is \(10\) ms^-1 and its base makes an angle \(\alpha=60^\circ\) with horizontal, then the vertical velocity of its end \(\mathrm{B}\) (in ms^-1) will be: