Question

A rigid rod is placed against the wall as shown in the figure. When velocity of its lower end is 10 m/s and its base makes an angle \(\alpha\) =60° with horizontal, then the vertical velocity of its end B will be

Answer 1

\(x^2+y^2=l^2\)

differentiate

\(2x\dfrac{dx}{dt}+2y\dfrac{dy}{dt}=0\)

\(2x*v_a+2y*v_b=0\)

use trig to get rid of x and y

\(x=l*cos \alpha\)

\(y=l*sin \alpha\)

\(2(l*cos \alpha)*v_a+2(l*sin \alpha)*v_b=0\)

\(v_b=-\dfrac{2(l*cos \alpha)*v_a}{2(l*sin \alpha)}=-\dfrac{v_a}{tan\alpha}=-v_a*cot\alpha\)

Answer 2

Thanx @aaronq !