Question

two particles A and B are connected by a rigid rod AB . the rod slides along perpendicular rails . the velocity of A to the left is 10m/s. what is the velocity of b when angle between A and the rod is 600.

Answer 1

These two rods form a right angled triangle with height as the y axis and the base as the x axis.

The hypotenuse is a constant which is the length of the rod.

Let the hypotenuse be l then :

x² + y² = l²..........1

The velocity along y is that of B and that along x is that of A.

Let the velocity along y be V and that along x be U = 10m/s.

Differentiating equation 1 with respect to t for both sides we have :

2x dx/dt + 2y dy/dt = 0

dx/dt = U

dy/dt = V

Doing substitution we have :

2xU = - 2yV

Lets make V the subject of the equation :

V = - x/y U

This equals :

-U cot Ф since x/y = 1/tanФ

Our tan Ф = Tan 60° = 1.3764

1/1.3764 = 0.7265

V = - 10 × 0.7265 = - 7.265 m/s

Answer 2

Please find the answer below:

Keeping in view that, two particles A and B are connected by a rigid rod AB . The rod slides along perpendicular rails. The velocity of A to the left is 10m/s.

The velocity of b when angle between A and the rod is 600= 5.8m/s