A rod of length 'l' is inclined at an angle 'theta' with the floor against a smooth vertical wall. If the end A moves instantaneously with velocity v_(1), what is the velocity of end B at the instant when rod makes 'theta' angle with the horizontal.

A rod of length 'l' is inclined at an angle 'theta' with the floor aga

1.	A rod of length 'l' is inclined at an angle 'theta' with the floor against a smooth vertical wall. If the end A moves instantaneously with velocity v_(1), what is the velocity of end B at the instant when rod makes 'theta' angle with the horizontal.
Answer» Solution :Let at any instant, end B and A are at a DISTANCE x and y respectively from the point .O.. Thus we have, `x^(2)+y^(2)=l^(2)"…………..(1)"` Here l is the length of the rod, which is CONSTANT. Differentiating eq (1) with RESPECT to time, we get `(d)/(dt)(x^(2)+y^(2))=(d)/(dt)(l^(2)), 2x(dx)/(dt)+2y(dy)/(dt)=0` If `(dx)/(dt)=v_(2) and (dy)/(dt)=-v_(1)` `x(v_(2))+y(-v_(1))=0` `rArr v_(2)=((y)/(x))v_(1)=v_(1)tan theta`